Generate Random Color distinguishable to Humans

The easiest way to pick maximally different colors would be to to use HSL values instead of RGB and then manipulate Hue, as it has a value from 0 to 360 value and wraps around (0 is red, and so is 360);

if you need 10 distinguishable colors you can divide 360 by 10 and then pick the individual color by multiplying the value by index (zero based). Here's an example function that allows you to pick a color from :

function selectColor(colorNum, colors){
    if (colors < 1) colors = 1; // defaults to one color - avoid divide by zero
    return "hsl(" + (colorNum * (360 / colors) % 360) + ",100%,50%)";
}

This way you can randomize the color selection by randomizing index, but colors will always be in the same palette.

This will select a random color from a palette of 10:

var color = selectColor(Math.floor(Math.random() * 10), 10);

and so will this:

var color = selectColor(Math.floor(Math.random() * 999), 10);

or you can select a specific color from the palette, like 9th color (index 8) out of palette of 13:

var color = selectColor(8, 13);

Here's a fiddle to play with: http://jsfiddle.net/2UE2B/

Update on 2020-02-23:

So, today I needed a solution to this same problem. Googling for this answer here (I know, a very weird way to look for stuff on SO) I ran into the Golden Angle concept. It would make the above example even more trivial, and would not require a predetermined number of colors to be provided:

function selectColor(number) {
  const hue = number * 137.508; // use golden angle approximation
  return `hsl(${hue},50%,75%)`;
}

This answers the @netoperator-wibby's question


You could use a fixed set of colors, such as the ones listed in the jquery.color.js plugin.

List of colors from jquery.color.js plugin:

Colors = {};
Colors.names = {
    aqua: "#00ffff",
    azure: "#f0ffff",
    beige: "#f5f5dc",
    black: "#000000",
    blue: "#0000ff",
    brown: "#a52a2a",
    cyan: "#00ffff",
    darkblue: "#00008b",
    darkcyan: "#008b8b",
    darkgrey: "#a9a9a9",
    darkgreen: "#006400",
    darkkhaki: "#bdb76b",
    darkmagenta: "#8b008b",
    darkolivegreen: "#556b2f",
    darkorange: "#ff8c00",
    darkorchid: "#9932cc",
    darkred: "#8b0000",
    darksalmon: "#e9967a",
    darkviolet: "#9400d3",
    fuchsia: "#ff00ff",
    gold: "#ffd700",
    green: "#008000",
    indigo: "#4b0082",
    khaki: "#f0e68c",
    lightblue: "#add8e6",
    lightcyan: "#e0ffff",
    lightgreen: "#90ee90",
    lightgrey: "#d3d3d3",
    lightpink: "#ffb6c1",
    lightyellow: "#ffffe0",
    lime: "#00ff00",
    magenta: "#ff00ff",
    maroon: "#800000",
    navy: "#000080",
    olive: "#808000",
    orange: "#ffa500",
    pink: "#ffc0cb",
    purple: "#800080",
    violet: "#800080",
    red: "#ff0000",
    silver: "#c0c0c0",
    white: "#ffffff",
    yellow: "#ffff00"
};

The rest is simply picking a random property from a Javascript object.

Colors.random = function() {
    var result;
    var count = 0;
    for (var prop in this.names)
        if (Math.random() < 1/++count)
           result = prop;
    return result;
};

Using Colors.random() might get you a human-readable color. I even powered an example below.

(function(){
    Colors = {};
    Colors.names = {
        aqua: "#00ffff",
        azure: "#f0ffff",
        beige: "#f5f5dc",
        black: "#000000",
        blue: "#0000ff",
        brown: "#a52a2a",
        cyan: "#00ffff",
        darkblue: "#00008b",
        darkcyan: "#008b8b",
        darkgrey: "#a9a9a9",
        darkgreen: "#006400",
        darkkhaki: "#bdb76b",
        darkmagenta: "#8b008b",
        darkolivegreen: "#556b2f",
        darkorange: "#ff8c00",
        darkorchid: "#9932cc",
        darkred: "#8b0000",
        darksalmon: "#e9967a",
        darkviolet: "#9400d3",
        fuchsia: "#ff00ff",
        gold: "#ffd700",
        green: "#008000",
        indigo: "#4b0082",
        khaki: "#f0e68c",
        lightblue: "#add8e6",
        lightcyan: "#e0ffff",
        lightgreen: "#90ee90",
        lightgrey: "#d3d3d3",
        lightpink: "#ffb6c1",
        lightyellow: "#ffffe0",
        lime: "#00ff00",
        magenta: "#ff00ff",
        maroon: "#800000",
        navy: "#000080",
        olive: "#808000",
        orange: "#ffa500",
        pink: "#ffc0cb",
        purple: "#800080",
        violet: "#800080",
        red: "#ff0000",
        silver: "#c0c0c0",
        white: "#ffffff",
        yellow: "#ffff00"
    };
    Colors.random = function() {
        var result;
        var count = 0;
        for (var prop in this.names)
            if (Math.random() < 1/++count)
               result = prop;
        return { name: result, rgb: this.names[result]};
    };
    var $placeholder = $(".placeholder");
    $placeholder.click(function(){
        var color = Colors.random();
        $placeholder.css({'background-color': color.rgb});
        $("#color").html("It's " + color.name);
    });
})();
.placeholder {
    width: 150px;
    height: 150px;
    border: 1px solid black;
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div class="placeholder"></div>
<span id="color">Click the square above.</span>

Example

I know I'm very late to this party, but I wrote up a more elaborate function to generate a set of contrasting random colors for another project. They are both (at least somewhat) attractive and genuinely random (not based on predefined colors) but my code is a bit more complicated than some of the other responses (so it's not for just getting the basics)

This is for users who want to have more than one random color on their page, and want to make sure no two colors are too similar.

Fiddle

var generateRandomColors=function(number){
/*
This generates colors using the following algorithm:
Each time you create a color:
    Create a random, but attractive, color{
        Red, Green, and Blue are set to random luminosity.
        One random value is reduced significantly to prevent grayscale.
        Another is increased by a random amount up to 100%.
        They are mapped to a random total luminosity in a medium-high range (bright but not white).
    }
    Check for similarity to other colors{
        Check if the colors are very close together in value.
        Check if the colors are of similar hue and saturation.
        Check if the colors are of similar luminosity.
        If the random color is too similar to another,
        and there is still a good opportunity to change it:
            Change the hue of the random color and try again.
    }
    Output array of all colors generated
*/
    //if we've passed preloaded colors and they're in hex format
    if(typeof(arguments[1])!='undefined'&&arguments[1].constructor==Array&&arguments[1][0]&&arguments[1][0].constructor!=Array){
        for(var i=0;i<arguments[1].length;i++){ //for all the passed colors
            var vals = /^#?([0-9a-f]{2})([0-9a-f]{2})([0-9a-f]{2})$/i.exec(arguments[1][i]); //get RGB values
            arguments[1][i]=[parseInt(vals[1], 16),parseInt(vals[2], 16),parseInt(vals[3], 16)]; //and convert them to base 10
        }
    }
    var loadedColors=typeof(arguments[1])=='undefined'?[]:arguments[1],//predefine colors in the set
        number=number+loadedColors.length,//reset number to include the colors already passed
        lastLoadedReduction=Math.floor(Math.random()*3),//set a random value to be the first to decrease
        rgbToHSL=function(rgb){//converts [r,g,b] into [h,s,l]
            var r=rgb[0],g=rgb[1],b=rgb[2],cMax=Math.max(r,g,b),cMin=Math.min(r,g,b),delta=cMax-cMin,l=(cMax+cMin)/2,h=0,s=0;if(delta==0)h=0;else if(cMax==r)h=60*((g-b)/delta%6);else if(cMax==g)h=60*((b-r)/delta+2);else h=60*((r-g)/delta+4);if(delta==0)s=0;else s=delta/(1-Math.abs(2*l-1));return[h,s,l]
        },hslToRGB=function(hsl){//converts [h,s,l] into [r,g,b]
            var h=hsl[0],s=hsl[1],l=hsl[2],c=(1-Math.abs(2*l-1))*s,x=c*(1-Math.abs(h/60%2-1)),m=l-c/2,r,g,b;if(h<60){r=c;g=x;b=0}else if(h<120){r=x;g=c;b=0}else if(h<180){r=0;g=c;b=x}else if(h<240){r=0;g=x;b=c}else if(h<300){r=x;g=0;b=c}else{r=c;g=0;b=x}return[r,g,b]
        },shiftHue=function(rgb,degree){//shifts [r,g,b] by a number of degrees
            var hsl=rgbToHSL(rgb); //convert to hue/saturation/luminosity to modify hue
            hsl[0]+=degree; //increment the hue
            if(hsl[0]>360){ //if it's too high
                hsl[0]-=360 //decrease it mod 360
            }else if(hsl[0]<0){ //if it's too low
                hsl[0]+=360 //increase it mod 360
            }
            return hslToRGB(hsl); //convert back to rgb
        },differenceRecursions={//stores recursion data, so if all else fails we can use one of the hues already generated
            differences:[],//used to calculate the most distant hue
            values:[]//used to store the actual colors
        },fixDifference=function(color){//recursively asserts that the current color is distinctive
            if(differenceRecursions.values.length>23){//first, check if this is the 25th recursion or higher. (can we try any more unique hues?)
                //if so, get the biggest value in differences that we have and its corresponding value
                var ret=differenceRecursions.values[differenceRecursions.differences.indexOf(Math.max.apply(null,differenceRecursions.differences))];
                differenceRecursions={differences:[],values:[]}; //then reset the recursions array, because we're done now
                return ret; //and then return up the recursion chain
            } //okay, so we still have some hues to try.
            var differences=[]; //an array of the "difference" numbers we're going to generate.
            for(var i=0;i<loadedColors.length;i++){ //for all the colors we've generated so far
                var difference=loadedColors[i].map(function(value,index){ //for each value (red,green,blue)
                    return Math.abs(value-color[index]) //replace it with the difference in that value between the two colors
                }),sumFunction=function(sum,value){ //function for adding up arrays
                    return sum+value
                },sumDifference=difference.reduce(sumFunction), //add up the difference array
                loadedColorLuminosity=loadedColors[i].reduce(sumFunction), //get the total luminosity of the already generated color
                currentColorLuminosity=color.reduce(sumFunction), //get the total luminosity of the current color
                lumDifference=Math.abs(loadedColorLuminosity-currentColorLuminosity), //get the difference in luminosity between the two
                //how close are these two colors to being the same luminosity and saturation?
                differenceRange=Math.max.apply(null,difference)-Math.min.apply(null,difference),
                luminosityFactor=50, //how much difference in luminosity the human eye should be able to detect easily
                rangeFactor=75; //how much difference in luminosity and saturation the human eye should be able to dect easily
                if(luminosityFactor/(lumDifference+1)*rangeFactor/(differenceRange+1)>1){ //if there's a problem with range or luminosity
                    //set the biggest difference for these colors to be whatever is most significant
                    differences.push(Math.min(differenceRange+lumDifference,sumDifference));
                }
                differences.push(sumDifference); //otherwise output the raw difference in RGB values
            }
            var breakdownAt=64, //if you're generating this many colors or more, don't try so hard to make unique hues, because you might fail.
            breakdownFactor=25, //how much should additional colors decrease the acceptable difference
            shiftByDegrees=15, //how many degrees of hue should we iterate through if this fails
            acceptableDifference=250, //how much difference is unacceptable between colors
            breakVal=loadedColors.length/number*(number-breakdownAt), //break down progressively (if it's the second color, you can still make it a unique hue)
            totalDifference=Math.min.apply(null,differences); //get the color closest to the current color
            if(totalDifference>acceptableDifference-(breakVal<0?0:breakVal)*breakdownFactor){ //if the current color is acceptable
                differenceRecursions={differences:[],values:[]} //reset the recursions object, because we're done
                return color; //and return that color
            } //otherwise the current color is too much like another
            //start by adding this recursion's data into the recursions object
            differenceRecursions.differences.push(totalDifference);
            differenceRecursions.values.push(color);
            color=shiftHue(color,shiftByDegrees); //then increment the color's hue
            return fixDifference(color); //and try again
        },color=function(){ //generate a random color
            var scale=function(x){ //maps [0,1] to [300,510]
                return x*210+300 //(no brighter than #ff0 or #0ff or #f0f, but still pretty bright)
            },randVal=function(){ //random value between 300 and 510
                return Math.floor(scale(Math.random()))
            },luminosity=randVal(), //random luminosity
                red=randVal(), //random color values
                green=randVal(), //these could be any random integer but we'll use the same function as for luminosity
                blue=randVal(),
                rescale, //we'll define this later
                thisColor=[red,green,blue], //an array of the random values
                /*
                #ff0 and #9e0 are not the same colors, but they are on the same range of the spectrum, namely without blue.
                Try to choose colors such that consecutive colors are on different ranges of the spectrum.
                This shouldn't always happen, but it should happen more often then not.
                Using a factor of 2.3, we'll only get the same range of spectrum 15% of the time.
                */
                valueToReduce=Math.floor(lastLoadedReduction+1+Math.random()*2.3)%3, //which value to reduce
                /*
                Because 300 and 510 are fairly close in reference to zero,
                increase one of the remaining values by some arbitrary percent betweeen 0% and 100%,
                so that our remaining two values can be somewhat different.
                */
                valueToIncrease=Math.floor(valueToIncrease+1+Math.random()*2)%3, //which value to increase (not the one we reduced)
                increaseBy=Math.random()+1; //how much to increase it by
            lastLoadedReduction=valueToReduce; //next time we make a color, try not to reduce the same one
            thisColor[valueToReduce]=Math.floor(thisColor[valueToReduce]/16); //reduce one of the values
            thisColor[valueToIncrease]=Math.ceil(thisColor[valueToIncrease]*increaseBy) //increase one of the values
            rescale=function(x){ //now, rescale the random numbers so that our output color has the luminosity we want
                return x*luminosity/thisColor.reduce(function(a,b){return a+b}) //sum red, green, and blue to get the total luminosity
            };
            thisColor=fixDifference(thisColor.map(function(a){return rescale(a)})); //fix the hue so that our color is recognizable
            if(Math.max.apply(null,thisColor)>255){ //if any values are too large
                rescale=function(x){ //rescale the numbers to legitimate hex values
                    return x*255/Math.max.apply(null,thisColor)
                }
                thisColor=thisColor.map(function(a){return rescale(a)});
            }
            return thisColor;
        };
    for(var i=loadedColors.length;i<number;i++){ //Start with our predefined colors or 0, and generate the correct number of colors.
        loadedColors.push(color().map(function(value){ //for each new color
            return Math.round(value) //round RGB values to integers
        }));
    }
    //then, after you've made all your colors, convert them to hex codes and return them.
    return loadedColors.map(function(color){
        var hx=function(c){ //for each value
            var h=c.toString(16);//then convert it to a hex code
            return h.length<2?'0'+h:h//and assert that it's two digits
        }
        return "#"+hx(color[0])+hx(color[1])+hx(color[2]); //then return the hex code
    });
}

Please note, although I don't do so in my example, that this can also be used to add new distinct, random colors to a set:

generateRandomColors(1,generateRandomColors(10))