Bubblegum Crisis was my favorite series back around 15 years ago, the time in my life when I watched anime. A big part of it, of course, was that the woman who voiced Priss had a hellasexy voice. But the series was entertaining apart from that as well, and I bought the series when it first became available on DVD.
The hard part about anime is that it is like American movies and there are movies and shows that span ALL genres.
I started out watching anime back in the early to mid 90s. So many of my favorite series are ones that were out at the time.
Depending on what genre you like, these may be good suggestions for you or bad ones. It also depends if you are willing to read subtitles (which after awhile most fan prefer because it opens up so much more) or dubbed.
Most movies from Studio Ghilbi
I second Ranma 1/2 and Nadesico
Series (if it has not already been mentioned):
Tenchi Muyo (and all 30 some spin-offs 
J/K)
Slayers
Bleach (if it has not already been mentioned)
Naruto
Kiddy Grade
Oh! My Goddess (AA! Megami Sama)
Hell Girl
Currently in fansubs:
Puella Magi Madoka Magica
Sorry ran out of time to post this. But once you have the genre that you like, check out http://animenfo.com for suggestions. They are a really good site for anime information.