Eh, my parents are somewhat anti-anime, so finding time to watch it isn't easy... I s'pose I could make a top 5 though, though I'm yet to sample so many shows ^^
1. Tonari no Totoro
Mreh, beautiful film, better than any other kids film I've seen... In fact, it's barely fair to call it a kids film, it's too uneventful for your average kid's attention span, it has appeal to people like me who despite having grown up are still children at heart
2. Azumanga Daioh
I'd suppose it's largely like it or loathe it, I know a lot of big anime fans who nevertheless really don't like Azumanga Daioh, but to me certainly, it was just so
funny. It almost made me wish I had a few more years of high school left...almost :P
3. Neon Genesis Evangelion
I remember reading somewhere that Gainax began to run out of money towards the end of Evangelion, so the last few episodes are somewhat lower budget or something. Truth be known I didn't notice, in fact, pretty soon into the series, I sort of forgot it was animated at all. It's one of the most gripping shows, anime or nay, I've ever watched, and contrary to a lot of peoples opinions, I actually really, really liked the ending...made me think a lot. The only reason it's not my favourite is because it's such an emotional endeavour to watch...
4. Grave of the Fireflies
Because I'm a big crybaby at heart, and Grave of the Fireflies is just one of the saddest, most disturbing films I've ever seen... I cry a fair bit, but rarely at films, Grave was an exception... It's just a wonderful anti-war statement, as well as an entertaining, if utterly melancholy, film. I've never watched it since the first time I saw it, and I'm not sure if I ever will. To put myself through the anguish of doing so again is not something I relish the thought of doing...
5. Vision of Escaflowne
Woo, I had a heck of a time watching this one ^^ As a love story, Escaflowne succeeds magnificently, but also manages to tell a truly intriguing and well plotted fantasy story, with a wonderful cast to boot... It's also just got the coolest soundtrack ever
Other anime I like are Shaman King, Inuyasha, Ranma 1/2, Fruits Basket and Love Hina. As well as all of Studio Ghibli's films. Come January I'll have a better PC and I should be able to watch more ^_^