In my humble opinion the best way is to just add a full day in milliseconds, depending on how you factor your code it can mess up if you are on the last day of the month.

For example Feb 28 or march 31.

Here is an example of how I would do it:

var current = new Date(); //'Mar 11 2015' current.getTime() = 1426060964567
var followingDay = new Date(current.getTime() + 86400000); // + 1 day in ms
followingDay.toLocaleDateString();

Imho this insures accuracy

Here is another example. I do not like that. It can work for you but not as clean as example above.

var today = new Date('12/31/2015');
var tomorrow = new Date(today);
tomorrow.setDate(today.getDate()+1);
tomorrow.toLocaleDateString();

Imho this === 'POOP'

So some of you have had gripes about my millisecond approach because of day light savings time. So I'm going to bash this out. First, Some countries and states do not have Day light savings time. Second Adding exactly 24 hours is a full day. If the date number does not change once a year but then gets fixed 6 months later I don't see a problem there. But for the purpose of being definite and having to deal with allot the evil Date() I have thought this through and now thoroughly hate Date. So this is my new Approach.

var dd = new Date(); // or any date and time you care about 
var dateArray =  dd.toISOString().split('T')[0].split('-').concat( dd.toISOString().split('T')[1].split(':') );
// ["2016", "07", "04", "00", "17", "58.849Z"] at Z 

Now for the fun part!

var date = { 
    day: dateArray[2],
    month: dateArray[1],
    year: dateArray[0],
    hour: dateArray[3],
    minutes: dateArray[4],
    seconds:dateArray[5].split('.')[0],
    milliseconds: dateArray[5].split('.')[1].replace('Z','')
}

Now we have our Official Valid international Date Object clearly written out at Zulu meridian. Now to change the date

dd.setDate(dd.getDate()+1); // this gives you one full calendar date forward
tomorrow.setDate(dd.getTime() + 86400000);// this gives your 24 hours into the future. do what you want with it.

var myDate = new Date();

//add a day to the date
myDate.setDate(myDate.getDate() + 1);

The Date constructor that takes a single number is expecting the number of milliseconds since December 31st, 1969.

Date.getDate() returns the day index for the current date object. In your example, the day is 30. The final expression is 31, therefore it's returning 31 milliseconds after December 31st, 1969.

A simple solution using your existing approach is to use Date.getTime() instead. Then, add a days worth of milliseconds instead of 1.

For example,

var dateString = 'Mon Jun 30 2014 00:00:00';

var startDate = new Date(dateString);

// seconds * minutes * hours * milliseconds = 1 day 
var day = 60 * 60 * 24 * 1000;

var endDate = new Date(startDate.getTime() + day);

JSFiddle

Please note that this solution doesn't handle edge cases related to daylight savings, leap years, etc. It is always a more cost effective approach to instead, use a mature open source library like moment.js to handle everything.

I use something like:

new Date(dateObject.getTime() + amountOfDays * 24 * 60 * 60 * 1000)

Works with day saving time:

new Date(new Date(2014, 2, 29, 20, 0, 0).getTime() + 1 * 24 * 60 * 60 * 1000)

Works with new year:

new Date(new Date(2014, 11, 31, 20, 0, 0).getTime() + 1 * 24 * 60 * 60 * 1000)

It can be parametrized:

function DateAdd(source, amount, step) {
  var factor = 1;
  if (step == "day") factor = 24 * 60 * 60 * 1000;
  else if (step == "hour") factor = 60 * 60 * 1000;
  ...
  new Date(source.getTime() + amount * factor);
}

You have to use the getDate() and setDate() methods of the Date object which respectively get and set the day value of the date.

var date = new Date();
date.setDate(date.getDate() + 1);

Check the MDC Date object reference for more information on working with dates