Just leverage the built-in toISOString method that brings your date to the ISO 8601 format:

let yourDate = new Date()
yourDate.toISOString().split('T')[0]

Where yourDate is your date object.

Edit: @exbuddha wrote this to handle time zone in the comments:

const offset = yourDate.getTimezoneOffset()
yourDate = new Date(yourDate.getTime() - (offset*60*1000))
return yourDate.toISOString().split('T')[0]

Try this; bear in mind that JavaScript months are 0-indexed, whilst days are 1-indexed.

var date = new Date('2010-10-11T00:00:00+05:30');
    alert(((date.getMonth() > 8) ? (date.getMonth() + 1) : ('0' + (date.getMonth() + 1))) + '/' + ((date.getDate() > 9) ? date.getDate() : ('0' + date.getDate())) + '/' + date.getFullYear());

From ES6 onwards you can use template strings to make it a little shorter:

var now = new Date();
var todayString = `${now.getFullYear()}-${now.getMonth()}-${now.getDate()}`;

This solution does not zero pad. Look to the other good answers to see how to do that.

MM/DD/YYYY format

If you have the MM/DD/YYYY format which is default for JavaScript, you can simply pass your string to Date(string) constructor. It will parse it for you.

Copyvar dateString = "10/23/2015"; // Oct 23

var dateObject = new Date(dateString);

document.body.innerHTML = dateObject.toString();

DD/MM/YYYY format - manually

If you work with this format, then you can split the date in order to get day, month and year separately and then use it in another constructor - Date(year, month, day):

Copyvar dateString = "23/10/2015"; // Oct 23

var dateParts = dateString.split("/");

// month is 0-based, that's why we need dataParts[1] - 1
var dateObject = new Date(+dateParts[2], dateParts[1] - 1, +dateParts[0]); 

document.body.innerHTML = dateObject.toString();

For more information, you can read article about Date at Mozilla Developer Network.

DD/MM/YYYY - using moment.js library

Alternatively, you can use moment.js library, which is probably the most popular library to parse and operate with date and time in JavaScript:

Copyvar dateString = "23/10/2015"; // Oct 23

var dateMomentObject = moment(dateString, "DD/MM/YYYY"); // 1st argument - string, 2nd argument - format
var dateObject = dateMomentObject.toDate(); // convert moment.js object to Date object

document.body.innerHTML = dateObject.toString();

Copy<script src="https://momentjs.com/downloads/moment.min.js"></script>

In all three examples dateObject variable contains an object of type Date, which represents a moment in time and can be further converted to any string format.