Your top 3 favorite move animations

Gunk Shot. What kind of a question is this? You throw a literal trashcan at the pokemon.

For me, I'd say:

1) Confusion: it looks terrifyingly awesome, as if it is ripping a hole out of the fabric of space itself. Plus, I like the way it sounds, too. =P

2) Sky Attack: The animation and sound of it looks as if you're traveling at the speed of light. Can't get any more badass than that!

3) Yawn: There's never a time when I'm not laughing whenever I see and hear this move lmaooo

Present ... is funny! A present is hurled at you.
Submission ... not sure if this has changed. Originally caused your pokemon to disappear into a spinning thing. Very confusing.
Magnet Bomb ... looks pretty cool.

Psycho Cut with Mewtwo - looks like back handing his foes like cmon!

Draco Meteor - as others have said

Solar beam is pretty sweet as well.

Oooh, good one. Mine:

1. Signal Beam: prismatic death ray
2. Sky Attack: WHOOSH!
3. Draining Kiss: when will-'o'-wisps attack

Of course, I also love Gunk Shot. Hex is also cool, as it looks like a dark ritual. And Volt Switch (how I wish you could dodge with it). There are even some animations I never get to see, so maybe I would like those, too.

It would be great if this site had a visual record of every animation, sort of like how some online dictionaries have a pronunciation audio snippet for words.

Silver wind, it looks like a big grey storm, its awesome

I like alot of these already mentioned. I'd also add Snarl, Struggle Bug and Psybeam. Psychic ''sounds'' cool too

Bonus: Volt Switch is the worst

1. Solar Beam - What BlameScott said. Orbital strike from the Death Star is so cool

2. Stone Edge - I love that it's so quick. Like BAM! A mountain pops out of nowhere, and still time to dodge the next attack.

3. Gardevoir's Dazzling Gleam - She kinda strikes a Marilyn Monroe type of pose with wind blowing from beneath her dress, but it's more of an angry, furious pose. like, "You dare fuck with me? I don't care if you've descended from the Ozone layer! Be dazzled from my gleam!"

Confusion before they changed it - when the defender used it against you. It hurt a lot too when it was 20 damage. I liked the shattered mirror effect.

I still like the munch munch munch animation of Crunch.

I have more than 3 favorite, cannot choose:

Sand Tomb - a realistic dust devil swirling around
Mirror Coat - a tiny mirror is being held up
Silver Wind - exactly what it says, all over the screen
Bug Buzz - weird transparent effects with particles
Power Whip - black strings lashing out
Gunk Shot - the trash can, my first fav, now on my 100% Muk
Vice Grip - chopper like in Prince of Persia unfortunately with little harm
Ancient Power - I saw a Lileep perform that to me, looks magical
Aqua Jet - saw this recently, was pleasantly surprised
Ice Beam - one of the nicest beams, dumping ice over the defender

And then there are also some cool Fire charge moves not sure which is which (Flame Wheel, Charge or Burst?)
Many more moves I have hardly ever seen, like Wrap, Draining Kiss, Disarming Voice, Drill Peck, Horn Attack, Magnet Bomb, Night Shade, Ominous Wind, Sludge, Poison Fang, Icy Wind, Gyro Ball...

Does anyone know a video demonstrating the various animations?

A lot of good ones have been mentioned, but one that hasn't, unless I missed it, is Mewtwo's focus blast. You watch him focusing all his brain energy and then launching an incredibly powerful pink/purple lightning bolt. It reminds me of the battle with Mew in the first Pokemon movie.

1. Gunk shot - It doesn't get better than throwing a trash can at an opponent.
2. Present - Throwing presents at an opponent during battle is like something out of a slapstick movie. I never get tired of it.
3. Shadow Ball - Big, ominous looking energy balls fired at the opponent. Who wouldn't love that?

Some less common answers:

Dragon Pulse- it's way cooler than outrage, sad that Niantic didn't make it as strong.

Hyper Beam- I only wish it was like yellowish orange like in the anime instead of the white/purple beam it is depicted in game.

Fire Blast- again a very commanding move like dragon pulse, yet made not as strong as an alternative move Overheat

Ice Beam: a ray of Ice on the opponent is very cool!

Shadow Ball: Gengar is so awesome that it can throw a curve ball.

Gunk Shot: interesting animation, TRASH the opponent.

Heat Wave looks amazing.
Stone Edge, Blizzard and Earthquake look good, too.
Bubble Beam is awesome. Every time I fought Suicune I hoped it had Bubble Beam just for the bubbly... beam.

I also have to mention one fast move: Metal Claw. Dang, it' so cool! I definitely need to use Ursarings more often. Metal Claw effect combined with Ursaring's fast move animation (Bear hug! Bear hug! Bear hug!) looks brilliant and hilarious at the same time.

1) DIsarming voice - hurt others with bad kareoke skills. Just like real life
2) Gunk Shot - trow garbage at the opponent... brilliant
3) Earthquake - really cool