Meanwhile you can use the isSameOrAfter method:

moment('2010-10-20').isSameOrAfter('2010-10-20', 'day');

Docs: https://momentjs.com/docs/#/query/is-same-or-after/

You should be able to compare them directly.

var date = moment("2013-03-24")
var now = moment();

if (now > date) {
   // date is past
} else {
   // date is future
}

$(document).ready(function() {
  
  $('.compare').click(function(e) {
  
    var date = $('#date').val();
  
    var now = moment();
    var then = moment(date);
  
    if (now > then) {
      $('.result').text('Date is past');
    } else {
      $('.result').text('Date is future');
    }

  });

});

<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.10.3/moment.min.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.0/jquery.min.js"></script>



<input type="text" name="date" id="date" value="2014-12-18"  placeholder="yyyy-mm-dd">
<button class="compare">Compare date to current date</button>
<br>
<div class="result"></div>

Meanwhile you can use the isSameOrAfter method:

moment('2010-10-20').isSameOrAfter('2010-10-20', 'day');

Docs: https://momentjs.com/docs/#/query/is-same-or-after/

You can generalize to a function that prevents mutating the original objects:

/** Returns true if the first date is before the second one. */
function dateIsBefore(moment1: Moment, moment2: Moment): boolean {
  return moment1.clone().startOf('day') < moment2.clone().startOf('day')
}

BEWARE THE TIMEZONE

Using the date object to represent just-a-date straight away gets you into a huge excess precision problem. You need to manage time and timezone to keep them out, and they can sneak back in at any step. The accepted answer to this question falls into the trap.

A javascript date has no notion of timezone. It's a moment in time (ticks since the epoch) with handy (static) functions for translating to and from strings, using by default the "local" timezone of the device, or, if specified, UTC or another timezone. To represent just-a-date with a date object, you want your dates to represent UTC midnight at the start of the date in question. This is a common and necessary convention that lets you work with dates regardless of the season or timezone of their creation. So you need to be very vigilant to manage the notion of timezone, both when you create your midnight UTC Date object, and when you serialize it.

Lots of folks are confused by the default behaviour of the console. If you spray a date to the console, the output you see will include your timezone. This is just because the console calls toString() on your date, and toString() gives you a local represenation. The underlying date has no timezone! (So long as the time matches the timezone offset, you still have a midnight UTC date object)

Deserializing (or creating midnight UTC Date objects)

This is the rounding step, with the trick that there are two "right" answers. Most of the time, you will want your date to reflect the local timezone of the user. What's the date here where I am.. Users in NZ and US can click at the same time and usually get different dates. In that case, do this...

// create a date (utc midnight) reflecting the value of myDate and the environment's timezone offset.
new Date(Date.UTC(myDate.getFullYear(),myDate.getMonth(), myDate.getDate()));

Sometimes, international comparability trumps local accuracy. In that case, do this...

// the date in London of a moment in time. Device timezone is ignored.
new Date(Date.UTC(myDate.getUTCFullYear(), myDate.getUTCMonth(), myDate.getUTCDate()));

Deserialize a date

Often dates on the wire will be in the format YYYY-MM-DD. To deserialize them, do this...

var midnightUTCDate = new Date( dateString + 'T00:00:00Z');

Serializing

Having taken care to manage timezone when you create, you now need to be sure to keep timezone out when you convert back to a string representation. So you can safely use...

• toISOString()
• getUTCxxx()
• getTime() //returns a number with no time or timezone.
• .toLocaleDateString("fr",{timeZone:"UTC"}) // whatever locale you want, but ALWAYS UTC.

And totally avoid everything else, especially...

• getYear(),getMonth(),getDate()

So to answer your question, 7 years too late...

<input type="date" onchange="isInPast(event)">
<script>
var isInPast = function(event){
  var userEntered = new Date(event.target.valueAsNumber); // valueAsNumber has no time or timezone!
  var now = new Date();
  var today = new Date(Date.UTC(now.getUTCFullYear(), now.getUTCMonth(), now.getUTCDate() ));
  if(userEntered.getTime() < today.getTime())
    alert("date is past");
  else if(userEntered.getTime() == today.getTime())
    alert("date is today");
  else
    alert("date is future");

}
</script>

See it running...

Update 2022... free stuff with tests ...

The code below is now an npm package, Epoq. The code is on github. You're welcome :-)

Update 2019... free stuff...

Given the popularity of this answer, I've put it all in code. The following function returns a wrapped date object, and only exposes those functions that are safe to use with just-a-date.

Call it with a Date object and it will resolve to JustADate reflecting the timezone of the user. Call it with a string: if the string is an ISO 8601 with timezone specified, we'll just round off the time part. If timezone is not specified, we'll convert it to a date reflecting the local timezone, just as for date objects.

function JustADate(initDate){
  var utcMidnightDateObj = null
  // if no date supplied, use Now.
  if(!initDate)
    initDate = new Date();

  // if initDate specifies a timezone offset, or is already UTC, just keep the date part, reflecting the date _in that timezone_
  if(typeof initDate === "string" && initDate.match(/(-\d\d|(\+|-)\d{2}:\d{2}|Z)$/gm)){  
     utcMidnightDateObj = new Date( initDate.substring(0,10) + 'T00:00:00Z');
  } else {
    // if init date is not already a date object, feed it to the date constructor.
    if(!(initDate instanceof Date))
      initDate = new Date(initDate);
      // Vital Step! Strip time part. Create UTC midnight dateObj according to local timezone.
      utcMidnightDateObj = new Date(Date.UTC(initDate.getFullYear(),initDate.getMonth(), initDate.getDate()));
  }

  return {
    toISOString:()=>utcMidnightDateObj.toISOString(),
    getUTCDate:()=>utcMidnightDateObj.getUTCDate(),
    getUTCDay:()=>utcMidnightDateObj.getUTCDay(),
    getUTCFullYear:()=>utcMidnightDateObj.getUTCFullYear(),
    getUTCMonth:()=>utcMidnightDateObj.getUTCMonth(),
    setUTCDate:(arg)=>utcMidnightDateObj.setUTCDate(arg),
    setUTCFullYear:(arg)=>utcMidnightDateObj.setUTCFullYear(arg),
    setUTCMonth:(arg)=>utcMidnightDateObj.setUTCMonth(arg),
    addDays:(days)=>{
      utcMidnightDateObj.setUTCDate(utcMidnightDateObj.getUTCDate + days)
    },
    toString:()=>utcMidnightDateObj.toString(),
    toLocaleDateString:(locale,options)=>{
      options = options || {};
      options.timeZone = "UTC";
      locale = locale || "en-EN";
      return utcMidnightDateObj.toLocaleDateString(locale,options)
    }
  }
}


// if initDate already has a timezone, we'll just use the date part directly
console.log(JustADate('1963-11-22T12:30:00-06:00').toLocaleDateString())
// Test case from @prototype's comment
console.log("@prototype's issue fixed... " + JustADate('1963-11-22').toLocaleDateString())