Sadly, there is no flexible, built-in "format" method for JS Date objects, so you have to do it manually (or with a plug-in/library). Here is how you would do it manually:

function formatDate(dateVal) {
    var newDate = new Date(dateVal);

    var sMonth = padValue(newDate.getMonth() + 1);
    var sDay = padValue(newDate.getDate());
    var sYear = newDate.getFullYear();
    var sHour = newDate.getHours();
    var sMinute = padValue(newDate.getMinutes());
    var sAMPM = "AM";

    var iHourCheck = parseInt(sHour);

    if (iHourCheck > 12) {
        sAMPM = "PM";
        sHour = iHourCheck - 12;
    }
    else if (iHourCheck === 0) {
        sHour = "12";
    }

    sHour = padValue(sHour);

    return sMonth + "-" + sDay + "-" + sYear + " " + sHour + ":" + sMinute + " " + sAMPM;
}

function padValue(value) {
    return (value < 10) ? "0" + value : value;
}

Using your example date . . .

formatDate("Wed May 27 10:35:00 EDT 2015")  ===>  "05-27-2015 10:35 AM"

[Addendum 12/2022]: Here's a library to format dates using Intl.DateTimeFormat.

[Addendum 01/2024]: And here is a (ES-)Date manipulation library

Try something like this

var d = new Date,
    dformat = [d.getMonth()+1,
               d.getDate(),
               d.getFullYear()].join('/')+' '+
              [d.getHours(),
               d.getMinutes(),
               d.getSeconds()].join(':');

If you want leading zero's for values < 10, use this number extension

Number.prototype.padLeft = function(base,chr){
    var  len = (String(base || 10).length - String(this).length)+1;
    return len > 0? new Array(len).join(chr || '0')+this : this;
}
// usage
//=> 3..padLeft() => '03'
//=> 3..padLeft(100,'-') => '--3' 

Applied to the previous code:

var d = new Date,
    dformat = [(d.getMonth()+1).padLeft(),
               d.getDate().padLeft(),
               d.getFullYear()].join('/') +' ' +
              [d.getHours().padLeft(),
               d.getMinutes().padLeft(),
               d.getSeconds().padLeft()].join(':');
//=> dformat => '05/17/2012 10:52:21'

See this code in [jsfiddle][1]

[edit 2019] Using ES20xx, you can use a template literal and the new padStart string extension.

const dt = new Date();
const padL = (nr, len = 2, chr = `0`) => `${nr}`.padStart(2, chr);

console.log(`${
    padL(dt.getMonth()+1)}/${
    padL(dt.getDate())}/${
    dt.getFullYear()} ${
    padL(dt.getHours())}:${
    padL(dt.getMinutes())}:${
    padL(dt.getSeconds())}`
);

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]

You can fully format the string as mentioned in other posts. But I think your better off using the locale functions in the date object?

var d = new Date("2017-03-16T17:46:53.677"); 
console.log( d.toLocaleString() ); 

edit :

ISO 8601 ( the format you are constructing with ) states the time zone is appended at the end with a [{+|-}hh][:mm] at the end of the string.

so you could do this :

var tzOffset = "+07:00" 
var d = new Date("2017-03-16T17:46:53.677"+ tzOffset);
console.log(d.toLocaleString());
var d = new Date("2017-03-16T17:46:53.677"); //  assumes local time. 
console.log(d.toLocaleString());
var d = new Date("2017-03-16T17:46:53.677Z"); // UTC time
console.log(d.toLocaleString());

edit :

Just so you know the locale function displays the date and time in the manner of the users language and location. European date is dd/mm/yyyy and US is mm/dd/yyyy.

var d = new Date("2017-03-16T17:46:53.677");
console.log(d.toLocaleString("en-US"));
console.log(d.toLocaleString("en-GB"));