I never was a huge anime fan but then I did catch some shows on cable TV and they were pretty fun.
Cowboy Beebop, and any of the Gundam series but mostly Wing were my first exposure to Anime.
But wait Im forgetting the show I watched religously when I was ten, and didnt know was anime.
Other than those three I dont have any fascination with Japanese culture or other characteristic signs of anime fanage.
But I live and die for robotech.