Programmatically setting the name of a variable

This will do it:

for(var i = 1; i <= 100; i++) {
    eval("variable_" + i + " = " + i + ";");
}

eval is basically evil, but for such purpose it's OK to use it. (reference)

Live test case.

You are better off using an array

var variable = [];
for (var i=1; i <= 100; i++) {
  variable[i] = i;
}

Later, you can access the values using variable[1], variable[2] etc.

Here are a few methods:

Method 1: use eval

Here is the most direct method:

for(var i = 1; i <= 100; i++) {
  eval("var variable_" + i + " = " + i);
}
variable_1; // => 1

Disclaimer for the above method: I don't think this problem is a good candidate for using eval. If you do use eval, you should never allow user input to go into what you are evaling, or you could open your site to security risks. That mistake is the main reason people say eval is evil.

Method 2: use dynamically generated object properties

This is a much, much better way:

// If you want these variables to be global, then use `window` (if you're 
// in a browser) instead of your own object.
var obj = {};
for(var i = 1; i <= 100; i++) {
  obj["variable_" + i] = i;
}
obj.variable_1; // => 1

About the note in the comment about using window to create global variables: I would recommend against this, as it is a quick way to pollute your global scope and step on variables unwittingly.

Method 3: use an array

David suggested using an array. This is another great idea, and, depending on what you are trying to do, may be preferred:

var arr = [];
for(var i = 1; i <= 100; i++) {
  arr.push(i);
}
arr[0]; // => 1