Error:

Create empty array

var a = [];

Create array with elements

var a = [1, 2, 3];

Get number of elements in the array

// len is 3
var len = ['a', 'b', 'c'].length

Join elements of the array with string

// s is 'a/b/c'
var s = ['a', 'b', 'c'].join('/');

Remove element from the array

var a = [1, 2, 3, 4, 5];
// a is [1, 2, 5], b is [3, 4]
var b = a.splice(2, 2);

Remove last element from the array

var a = [1, 2, 3, 4, 5];
// last is 5 and a is [1, 2, 3, 4]
var last = a.pop();

Remove first element from the array

var a = [1, 2, 3, 4, 5];
// first is 1 and a is [2, 3, 4, 5]
var first = a.shift();

Add element to the end of the array

var a = [1, 2, 3, 4, 5];
// a is [1, 2, 3, 4, 5, 0]
a.push(0);

Add element to the beginning of the array

var a = [1, 2, 3, 4, 5];
// a is [0, 1, 2, 3, 4, 5]
a.unshift(0);

Get subarray of the array

var a = [1, 2, 3, 4, 5];
// suba is [ 3, 4 ]
var suba = a.slice(2, 4);

Replace subarray of the arary with another array

var a = [1, 2, 3, 4, 5];
// a is [1 ,2, 'a', 'b', 'c', 5]
a.splice(2, 2, 'a', 'b', 'c');

Iterate over all elements of the array

for (int i = 0; i < array.length; i++) {
    // handle array[i]
}

Get unique elements of the array

Array.prototype.unique= function(){
   var u = {}, a = [];
   for(var i = 0, l = this.length; i < l; ++i){
      if(u.hasOwnProperty(this[i])) {
         continue;
      }
      a.push(this[i]);
      u[this[i]] = 1;
   }
   return a;
}
// a is [ 1, 2, 3, 4, 5 ]
var a = [1, 2, 2, 2, 3, 4, 5, 5].unique();

Get difference between two arrays

Array.prototype.diff = function(a) {
    return this.filter(function(i) {return !(a.indexOf(i) > -1);});
};
// a is [1, 5]
var a = [1, 2, 3, 4, 5].diff( [2, 3, 4, 10, 11] );

Get intersection of two arrays

Array.prototype.intersection = function(a) {
    return this.filter(function(i) {return (a.indexOf(i) > -1);});
};
// a is [2, 3, 4]
var a = [1, 2, 3, 4, 5].intersection( [2, 3, 4, 10, 11] );

Append one array to another

// a is [ 1, 2, 2, 3 ]
var a = [1, 2].concat([2, 3]);

Reverse the array

// a is [3, 2, 1]
var a = [1, 2, 3].reverse();

Find all elements of the array that pass test

// find all even numbers
// a is [0, 2, 4]
var a = [0, 1, 2, 3, 4].filter(function(n) {
    return ((n % 2) === 0);
});

Sort the array numerically

// descending order
// a is [12, 11, 3, 2, 1]
var a = [11, 12, 1, 2, 3].sort(function(a,b){return b-a});

// ascending order
// a is [1, 2, 3, 11, 12]
var a = [11, 12, 1, 2, 3].sort(function(a,b){return a-b});

Sort the array lexically

// ascending order
// arr is ['One', 'Three', 'Two']
var arr = ['One', 'Two', 'Three'].sort(function(a,b){return a.localeCompare(b)});

// descending order
// arr is [ 'Two', 'Three', 'One' ]
var arr = ['One', 'Two', 'Three'].sort(function(a,b){return b.localeCompare(a)});

Shuffle the array

function shuffle(array) {
    var counter = array.length, temp, index;
    while (counter > 0) {
        index = Math.floor(Math.random() * counter);
        counter--;
        temp = array[counter];
        array[counter] = array[index];
        array[index] = temp;
    }

    return array;
}

var a = shuffle([0, 1, 2, 3, 4, 5]);

Map elements of the array

// a is [0, 1, 4, 9, 16, 25]
var a = [0, 1, 2, 3, 4, 5].map(function(a) {return a*a});

Check if the array contains the element

var hasItem = (a.indexOf(obj) !== -1);

Check whether all elements in the array pass the test

// allEven is false, 1 and 3 are odd
var allEven = [0, 1, 2, 3, 4].every(function(n) {return ((n % 2) === 0);});

// allEven is true
var allEven = [0, 2, 4].every(function(n) {return ((n % 2) === 0);});

Check whether at least one element in the array passes the test

// someEven is true
var someEven = [0, 1, 2, 3, 4].some(function(n) {return ((n % 2) === 0);});

Reduce array elements (left-to-right)

// sum is 10
var sum = [0,1,2,3,4].reduce(function(previousValue, currentValue, index, array){
  return previousValue + currentValue;
});

Reduce array elements (right-to-left)

// r is '43210'
var r = [0,1,2,3,4].reduceRight(function(previousValue, currentValue, index, array){
  return previousValue + currentValue.toString();
});

Perform function on every element of the array

// just print all elements
['One', 'Two', 'Three'].forEach(function(obj){
    console.log(obj);
});

Find maximum number in the array

Array.max = function( array ){
    return Math.max.apply( Math, array );
};

// m is 10
var m = Array.max([-1, 10, 0]);

Find minimum number in the array

Array.min = function( array ){
    return Math.min.apply( Math, array );
};

// m is -1
var m = Array.min([-1, 10, 0]);