Ooh, tough one...especially since I always have troiuble wondering whether to include movies, and how to compare how much I like a one-shot or short OVA compared to the glories of a 26-episode series. Not necessarily in this order, since once I get pas the top two, they fluctuate with my mood:
1. Fruits Basket, my true love.
2. Excel Saga, my naughty bit on the side
3. Tsukikage Ran, the funniest samurai tale ever.
4. Rune Soldier, comedy Dungeons and Dragons style.
5. Galaxy Angel, madness in space.
6. Dragon Half, only two episodes but almost as brilliantly wacky as Excel Saga. Way, way!
7. Read or Die/ R.O.D. the TV, I wanna be a paper master
8. Comic Party, if the US had stuff like this I'd never have stopped cartooning
9. Azumanga Daioh, probably on everyone's list somewhere
10. Eyeshield 21, wish they'd do a US release, darn it!
I don't read Manga nearly as much, but am fond of these ones I've read:
1. Fruits Basket, for beyond-the-seriesness
2. Excel saga for beyond-the-seriesness and alternate-universeness
3. Pet Shop of Horrors for beyond-the-seriesness and yaioish cuteness
4. Death Note for sheer coolness. I'm on #3
5. Yotsubato&! a worthy successor to Azumanga Daioh
Those are the only ones I remember especially liking, though I did read several others, briefly.