In no real order of preference,
FLCL - I love this show but am loathe to try to explain WHY.
Twelve Kingdoms - it took the "girl in a fantasy" story and actually made more realistic and WORK beautifully.
Visions of Escaflowne (the series, not the movie) - my first anime, I still have a soft spot for it
Vampire Hunter D: Bloodlust (a.k.a. the good one) - so pretty, plot wise its alright and D is awesome
Porco Roso - its one of the simpler Miyazaki films, the story line doesn't really surprise anyone but its still one of my favorites
My Neighbor Totoro - classic
Hellsing Ultimate OVA - I love vampires, Dracula and I have a love for over the top violence - this series pretty much gives me all that
Ouron High School Host Club - I love this series cause its self aware of the ridiculousness of the shoujo genre that its part of and its nice light entertainment. The anime equivalent of bubblegum and and cotton candy combined.