Get the element with the highest occurrence in an array

This is just the mode. Here's a quick, non-optimized solution. It should be O(n).

function mode(array)
{
    if(array.length == 0)
        return null;
    var modeMap = {};
    var maxEl = array[0], maxCount = 1;
    for(var i = 0; i < array.length; i++)
    {
        var el = array[i];
        if(modeMap[el] == null)
            modeMap[el] = 1;
        else
            modeMap[el]++;  
        if(modeMap[el] > maxCount)
        {
            maxEl = el;
            maxCount = modeMap[el];
        }
    }
    return maxEl;
}

There have been some developments in javascript since 2009 - I thought I'd add another option. I'm less concerned with efficiency until it's actually a problem so my definition of "elegant" code (as stipulated by the OP) favours readability - which is of course subjective...

function mode(arr){
    return arr.sort((a,b) =>
          arr.filter(v => v===a).length
        - arr.filter(v => v===b).length
    ).pop();
}

mode(['pear', 'apple', 'orange', 'apple']); // apple

In this particular example, should two or more elements of the set have equal occurrences then the one that appears latest in the array will be returned. It's also worth pointing out that it will modify your original array - which can be prevented if you wish with an Array.slice call beforehand.

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Edit: updated the example with some ES6 fat arrows because 2015 happened and I think they look pretty... If you are concerned with backwards compatibility you can find this in the revision history.

As per George Jempty's request to have the algorithm account for ties, I propose a modified version of Matthew Flaschen's algorithm.

function modeString(array) {
  if (array.length == 0) return null;

  var modeMap = {},
    maxEl = array[0],
    maxCount = 1;

  for (var i = 0; i < array.length; i++) {
    var el = array[i];

    if (modeMap[el] == null) modeMap[el] = 1;
    else modeMap[el]++;

    if (modeMap[el] > maxCount) {
      maxEl = el;
      maxCount = modeMap[el];
    } else if (modeMap[el] == maxCount) {
      maxEl += "&" + el;
      maxCount = modeMap[el];
    }
  }
  return maxEl;
}

This will now return a string with the mode element(s) delimited by a & symbol. When the result is received it can be split on that & element and you have your mode(s).

Another option would be to return an array of mode element(s) like so:

function modeArray(array) {
  if (array.length == 0) return null;
  var modeMap = {},
    maxCount = 1,
    modes = [];

  for (var i = 0; i < array.length; i++) {
    var el = array[i];

    if (modeMap[el] == null) modeMap[el] = 1;
    else modeMap[el]++;

    if (modeMap[el] > maxCount) {
      modes = [el];
      maxCount = modeMap[el];
    } else if (modeMap[el] == maxCount) {
      modes.push(el);
      maxCount = modeMap[el];
    }
  }
  return modes;
}

In the above example you would then be able to handle the result of the function as an array of modes.