I haven't watched many animes but I'm not going to go for the cliche dbz choice, I'll go with dragonball instead. I much preferred it anyway. I loved the sense of adventure it contained. Something Dragonball z lost. I also prefer the "slower" fighting.
Oh and this even though it's a fan-made anime.
Pokemon, of course, and also Keroro Gunso! That's awesome, as awesome as Leprechauns on a Rainbow with Gold Underneath, and Bunnies hopping in it! I have a disorder, it's called RFTW (Randomness for the win)!!!!!
I currently have two favorites: Claymore and Highschool of the Dead.
Claymore has amazing artwork and a nice story. I think what I love most is how it can make even the most gruesome scenes a work of art.
HSotD is just bloody zombie fun. It's absolutely genius in many ways and, again, has nice art. The downside is that it can get pretty sexual.... as most anime does, I guess. I dunno, it just made me uncomfortable. Other than that though, it's how I assume the ZA will go down.
Favorite anime would easily be FMA Brotherhood. Tons of reasons why I love it, but mostly because it has such a huge and diverse cast of characters that you really grow fond of. The 2003 version of FMA's plotline is pretty screwed up, but its still got Ed and Al (the main characters) who I absolutely adore for their humility, righteousness, quirkiness, fighting skillz, blah blah blah.
Technically not anime, but I also LOVE LOVE LOVE Avatar: the Last Airbender. I literally feel sorry for anyone who hasn't seen it, it's that good. Legend of Korra (the spin-off)'s ending is screwed up, but it still lives up to the Avatar tradition of excellence.
Detective Conan ~ I just love this anime, It's the kind of thing I have so many childhood memories from too. Pokemon, One Piece, Yu Gi Oh and this show I always watched as a kid. But for this show in particular I love the mystery/thriller theme.
1. DEATH NOTE
This anime is wonderful. It's so incredibly well done! If you haven't watched it, go watch it now. Or when you have time. Just make sure you watch it!
2. Ouran Highschool Host Club
This was my favorite until I watched Death Note. This one is a romance comedy sort of thing, and I freaking laugh my head off at parts of it.
3. The Melancholy of Haruhi Suzumiya
I admit some parts of this don't make any sense, but it's still pretty cool... It ended at a random spot, however... It's still pretty good, that is, if you think a reckless girl who is unaware she can control the universe while doing it is interesting. She never even discovers her powers... Eh, yeah.