Removes leading and trailing whitespace.

$.trim('    lots of extra whitespace    ');
// returns 'lots of extra whitespace'

Iterates over arrays and objects.

$.each([ 'foo', 'bar', 'baz' ], function(idx, val) {
    console.log('element ' + idx + 'is ' + val);
});

$.each({ foo : 'bar', baz : 'bim' }, function(k, v) {
    console.log(k + ' : ' + v);
});

Returns a value's index in an array, or -1 if the value is not in the array.

var myArray = [ 1, 2, 3, 5 ];

if ($.inArray(4, myArray) !== -1) {
    console.log('found it!');
}

Changes the properties of the first object using the properties of subsequent objects.

var firstObject = { foo : 'bar', a : 'b' };
var secondObject = { foo : 'baz' };

var newObject = $.extend(firstObject, secondObject);
console.log(firstObject.foo); // 'baz'
console.log(newObject.foo);   // 'baz'

If you don't want to change any of the objects you pass to $.extend, pass an empty object as the first argument.

var firstObject = { foo : 'bar', a : 'b' };
var secondObject = { foo : 'baz' };

var newObject = $.extend({}, firstObject, secondObject);
console.log(firstObject.foo); // 'bar'
console.log(newObject.foo);   // 'baz'

Returns a function that will always run in the provided scope — that is, sets the meaning of this inside the passed function to the second argument.

var myFunction = function() { console.log(this); };
var myObject = { foo : 'bar' };

myFunction(); // logs window object

var myProxyFunction = $.proxy(myFunction, myObject);
myProxyFunction(); // logs myObject object

If you have an object with methods, you can pass the object and the name of a method to return a function that will always run in the scope of the object.

var myObject = {
    myFn : function() {
        console.log(this);
    }
};

$('#foo').click(myObject.myFn); // logs DOM element #foo
$('#foo').click($.proxy(myObject, 'myFn')); // logs myObject