Is there a Javascript function similar to the Python Counter function?

You can use Lo-Dash's countBy function:

var list = ['a', 'b', 'c', 'b', 'a', 'b', 'c', 'a', 'a', 'a'];
console.log(_.countBy(list));

JSFiddle example

DIY JavaScript solution:

var list = ['a', 'b', 'c', 'b', 'a', 'b', 'c', 'a', 'a', 'a'];

function Counter(array) {
  var count = {};
  array.forEach(val => count[val] = (count[val] || 0) + 1);
  return count;
}

console.log(Counter(list));

JSFiddle example

Update:

Alternative that uses a constructor function:

var list = ['a', 'b', 'c', 'b', 'a', 'b', 'c', 'a', 'a', 'a'];

function Counter(array) {
  array.forEach(val => this[val] = (this[val] || 0) + 1);
}

console.log(new Counter(list));

JSFiddle example