Favorite anime is easy to list. Bubble Gum Crisis is right up there because it got me hooked on anime. In a game at the time I was running a character called Pristine (Pris for short), bad temper, road a motorcycle, girl with attitude who sang in a band. Some friends into anime also in the game said I had to see BGC, for obvious reasons.
I'm also a fan of Kotetsu, Phantom Quest Corp., El Hazard, the OAV's are excellent. For stuff you might not have seen yet, Read or Die is great, light hearted adventure coming to the US soon. Boogiepop Phantom I'm..still trying to decide. It's one of very few series to actuyally creep me out at times. Spirited Away was excellent. Excel Saga was not to my taste at all but I know people who loved it.
Personally, I'm a big fan of DBZ. It has drawbacks. Goku v. Frieza took -way- too long. the dubbing is not only verybad at times, but actually messes up the show (today's show, Wed the 13th, is a great example of this). It's also very watered down, everytime Vegita says 'Darn it!" I wince.

The power levels reach the point of being silly, but it's not as bad if you just keep thinking "It's a super hero anime, not a martial arts anime."
On the plus side it does things other long running anime rarely bother with. Characters age, get older, get married, have kids, their kids grow up, etc. Bulma starts out around 15 and by the end of DBZ she's in her 30's and looks it. Charactes develop and change but it often takes time. Vegita took a good 170 eps to grow up from a bad guy to a good guy.
DBZ is hardly perfect, but it's great fun.