I barely managed to shave the list down to 15.  
10 is impossible for me.  I had to leave some 
favorites off, but here's the current (subject to 
change within the next 5 minutes) list of 
favorite anime SERIES.  I didn't include any 
movies on this list because I consider many of 
the best anime movies to be on a different level 
than series, budget and story-wise.

Legend of the Galactic Heroes
Dragon Ball
Nintama Rantarou
Hunter x Hunter
One Piece
Detective Conan
Cyborg 009: Battle Alive
Ryu Knight
Trigun
Area 88
CLAMP Campus Detectives
Romeo's Blue Skies
Slayers series
Patlabor
Irresponsible Captain Tylor

I'm sure this list comes as a huge shock to those 
who know me.  ^_-

Jennifer