Zombie Brand, Blackthorn Morgana, Foxfire Ahri, Surprise Fiddlesticks, Pool Party Ziggs (Spell changes are cool)
Riot Graves, Pax Sivir, Fisherman Fizz (I am a sucker for exclusive skins)
I really like the old christmas skins, Reindeer Kog, Santa Gragas, Amumu Present (but started playing after those skins were vaulted, would like to see some old skins resurface)
Cryocore Brand, Mad Scientist Ziggs, Jailbreak Graves, Huntress Sivir, Full Metal Jayce, Blight Crystal Varus (Varus' original skin shouldn't exist), Urfrider Corki are additional skins I like
Finally, anything Rumble! Give me something fresh like Tristy being a T-Rex for the Jurassic theme (I will pay you all the moneys)

My favorite skin ever would have to be Hyena Warwick.

Everything about it, from the splash art, to the model, to its animations, to the sound effects... it's just perfect.

If we're including the splash art, I refuse to believe there is a better looking splash art than blood moon akali. If only in-game skin though, I've always liked spellthief Lux, Guqin, Arcade, and Pentakill Sona. >_> I may or may not really like Sona <_<

My favorite skin because of the genius behind it is: Definitely not Blitzcrank
My favorite skin that i actually have and use is: Iron Solari Leona or Tyrant Swain depending on my mood

Snowmerdinger without a doubt, too bad I wasn't around when it was on sale. I also really like Old Saint Zilean and Silent Night Sona.

I couldn't possibly choose; there are so many awesome skins.
I can tell you what all of them have in common though; they all are recognizable as the champion, but are a little more than a recolour or a different outfit
For example, Arcade Sona and Astronautilus look excellent, but their particle effects, and sounds are different as well. I particularly like how Arcade and Guqin Sona's stance songs match the sound of what her instrument is. It's nice to hear, and I even turn my music off to listen to it.
As well, the little things like changing what kind of sapling Maokai has or having Teemo's mushrooms be something else that make the skin that much more worthwhile. Having Swain and Shyvana's ultimates change to match their skin is also awesome (I love Darkflame Shyvana for that reason). Hell, even the little flag on Warlord Shen makes it great.
Obviously you can't make them completely different; that's what legendary skins are for. But the little differences add up and make the skins that much better.

My favorite is definitely Sad Robot Amumu.

Zombie Brand and Battlecast Cho are the best skins in the game right now imo. I don't own either of them though.

Out of the ones I do have, my favourites are Wicked Lulu (I'm a cat lover, and Pix looks awesome all bat-like), Blackthorn Morgana, Tyrant Swain and Arcade Sona.

Top 5 favourite skins

Gentleman Cho Gath
Full Metal Jayce
Astronaut Teemo
Veigar Graybeard
Cyborg Wukong (if they ever made that skin ;_; )

I'd have to say Headless Hecarim, Renegade Talon, Northern Front Swain, and Augmented Singed because they fit the original mold of the characters so well. It's easy to imagine Swain dressed like that for an invasion of frejlord, or Talon because he was already a street thug, so he'd be right at home in that kind of shabby, ragged attire. I'm sure Singed has tried atleast once to bulk himself up through alchemy, and Hecarim is already a rampaging "horseman".