This is one of those things that is so good, you almost want to keep it to yourself just to have your own secret weapon.  Unfortunately, the generous author of such an ActionScript library, Jack Doyle, is such a good programmer and has given so much to the community that I feel obligated to pay it forward.

IMHO- the Greensock Tweening Platform, TweenLite, TweenMax, etc... is the best animation engine and as3 utility library ever made.

The Fastest.
You can use the benchmarking application jack has on his site to test his engine with a particle generator script- check it's performance against Tweener, Flash, and other major tweening engines and the comparison is obvious- the particles fly fast and smooth at a much, MUCH higher count than any of the other engines can handle without looking like 3 fps.

The Easiest.
Besides being ridiculously easy to use with a quick 1-liner syntax, you can add event handlers and other interesting things all in line.  Here's a 1 second slide/fade in that cues a function called "nextAnimation()":

TweenLite.to(anyObject, 1, {x: 100, ease: Strong.easeOut, alpha: 1, onComplete: nextAnimation} );

The Smoothest.
Watch your animations slide across the screen smoothly with plenty of well optimized easing classes included with the library.

Thanks and kudos to Jack and his excellent work, the Greensock library has become a not-so-secret weapon for many flash developers. Check out the Greensock site to see how many other awesome classes you can get for things like full screen layouts, filter tweening, sequencing, easing, managing XML, and a lot more.

Get the Greensock Tweening Platform and other great actionscript classes here.