I watched things like Speed Racer and Tranzor Z growing up, but Dragonball Z is what really got me into anime. I look to Toonami for anime mostly, and I it out wherever I see it on tv.
But my favorites?
Dragonball Z is definately up there, in my opinion the best action cartoon of all time (with a nod to Batman, X-Men, and Spider-Man as honorable mentions)
But currently Cowboy Bebop is my favorite. Every episode is a short epic in itself, the cast is not too large, and all the characters have plenty of depth. The music is outstanding, and it'll make even the most jaded music lover turn up their tv when they play "Real Folk Blues"
The animation style is great, and there's plenty of action in there, as well as comedy, mystery, and romance. I hope Knockin' On Heaven's Door (the Cowboy Bebop movie) comes to the US on DVD soon!
-See you space cowboy...