An easy to understand and simple solution.

// Save today's date.
var today = DateTime.Today;

// Calculate the age.
var age = today.Year - birthdate.Year;

// Go back to the year in which the person was born in case of a leap year
if (birthdate.Date > today.AddYears(-age)) age--;

However, this assumes you are looking for the western idea of the age and not using East Asian reckoning.

Short & Snazzy:

+ new Date()

A unary operator like plus triggers the valueOf method in the Date object and it returns the timestamp (without any alteration).

Details:

On almost all current browsers you can use Date.now() to get the UTC timestamp in milliseconds; a notable exception to this is IE8 and earlier (see compatibility table).

You can easily make a shim for this, though:

if (!Date.now) {
    Date.now = function() { return new Date().getTime(); }
}

To get the timestamp in seconds, you can use:

Math.floor(Date.now() / 1000)

Or alternatively you could use:

Date.now() / 1000 | 0

Which should be slightly faster, but also less readable.
(also see this answer or this with further explaination to bitwise operators).

I would recommend using Date.now() (with compatibility shim). It's slightly better because it's shorter & doesn't create a new Date object. However, if you don't want a shim & maximum compatibility, you could use the "old" method to get the timestamp in milliseconds:

new Date().getTime()

Which you can then convert to seconds like this:

Math.round(new Date().getTime()/1000)

And you can also use the valueOf method which we showed above:

new Date().valueOf()

Timestamp in Milliseconds

var timeStampInMs = window.performance && window.performance.now && window.performance.timing && window.performance.timing.navigationStart ? window.performance.now() + window.performance.timing.navigationStart : Date.now();

console.log(timeStampInMs, Date.now());