I really haven't see too many animus, but here's what I did enjoy. I'll try to categorize them be genre or something.
ACTION/COMEDY
Trigun (yet to read the manga, but I plan to soon)
Beelzebub (I am so in love with both the manga and anime omfg I'm gay for Hilda)
DragonBall (I like the original more than Z but Z is okay too. Haven't read any of the manga.)
Xiaolin Sisters (random short manga I picked up at a flea market; worth a read if you can find it)
Panty and Stocking with Garterbelt (pervy and hilarious, and kickass music)
ACTION WITHOUT COMEDY
Saint Seiya (the original series. I haven't read any of the manga or seen the new series yet)
DRAMA/COMDEY
Ouran High School Host Club (anime and manga are both funny)
Pita-Ten (also fantasy since it's about angels and demons, read the manga, haven't seen the anime because they changed the ending)
FANTASY
Rozen Maiden (only read the manga, don't know if the anime is any good)
12 Kingdoms (the anime is great, I haven't read any of the novels it's based on, but I would like to)
Magic Knights Rayearth (only read the first fairly short series, but it was cool)
I can't think of a Studio Ghibli movie I didn't enjoy. A lot of the time they make references to Japanese mythology that I don't really get, but I just kind of sit back and enjoy the movie and don't think about it too hard. Which apparently is doing it wrong since the movies I guess all have deep messages or something but I have fun so whatevs.
MAGICAL GIRL
Sailor Moon (but really, if you're here and aren't even vaguely aware of this, then I don't know what to tell you)
Tokyo Mew Mew (anime and manga are both girly and cute)
Wedding Peach (AHAHAHAHAHAHAHAHA)
SLICE OF LIFE
Azumanga Daioh (saw the anime and read parts of the 4komas, both hilarous)
Uhh...that's all I can remember for now. I'll edit the list if I can remember more