I couldnt honestly tell you my favourite anime, but here are some series i have seen, and what i thought of them
Death Note - ****
The first season was brilliant, the second, not so much, though it was still entertaining.
Hellsing - ***1/2
Vampires, ah vampires. Alot more action in this one. unfortunately i felt the story didnt really develop properly throughout, only suddenly deveolped at the end of the series.
FLCL - ****1/2
a short series, but if you are at all into classic/indy rock then you will like the soundtrack to thus and alot of the jokes. Its a pretty chaotic, but the chaos is what makes it awesome
Tenjho Tenge ****
A fairly decent fighting series, with just enough fanservice to keep people interested, unfortunately again the series seemed to end prematurely
Ikki Tousen ***1/2
As action packed as Tenjho Tenge, but with alot more fanservice, and a story that is pretty intriguing for the most part, unfortunately the main character is almost completely useless, until randomly gets possessed by an ancient spirit etc etc
Project A-ko ***1/2
slightly older series, actually a series of 4 movies about a school girl called A-ko who has superhuman strength and her arch rival B-ko who is a bratty rich girl constantly building bigger and better robots to beat A-ko, all for the friendship of the most annoyingly voice character ever, C-ko (i know, not the most creative character naming)
A decent watch. Story about a young magician boy, who happens to have very powerful genes, but unfortunately can only use his magic 8 times in his life. but due to his incredible genetic makeup, every girl in his school wants to take his seed, three girls in particular from powerful family lines. These girls all end up falling for him and hilarity ensues
Midori Days - ****
guy wakes up one day with a girl who had a crush on his as his right hand, hilarity ensues. Not a bad series
Please Twins - ***1/2
highschool boy living alone in the house he grew up in, only to find a picture of him as a kid with his twin sister. Two girls show up at his door claiming to be his sister and both end up moving in with him until they can afford to get a DNA test done. of course they both fall for him and make a promise that if they find out they are not his brother, they will be allowed by the other to date him. Has a few tie ins to the next series ill talk about ..
Please Teacher (Onegai Teacher) - ****
Highschool boy withnesses an alien landing, the alien happening to be a hot lady, who turns out to be his teacher at school, but she is really there to observe human behaviour. To cover the fact that he knows her secret, they end up married and living together, and in the end falling in love.
Cowboy Bebop ****1/2
great show. gang of misfit bounty hunters travel the galaxy chasing bounties and running from/chasing their pasts. Its obvious the creator of this series was a fan of western movies, the cowboy references are abundant (as is probably obvious from the series title)
i could probably list a few more, but these are the ones i can think of at the moment