I'm a HUGE fan of anime, although lately, I haven't seen much anime. Last summer I bought these series and watched through them. Initial D, FLCL, Gunbuster 1, Gunbuster 2, and Ghost in the Shell (GitS) Solid State Society.
I've seen all GitS except the 2nd Gig, I've seen a BUNCH of anime over the years. I can recommend a variety of anime depending on particular tastes. I don't watch some kinds of anime though, like moe, harem, and hentai.
Funniest anime I ever saw : Magical Shopping Arcade Abenobashi and Dragon Ball (before Z or GT)
Best action: there's a few, Samurai 7, Golgo 13, Akira, DBZ, Gunbuster (1 and 2)
Best drama anime: Satoshi Kon is a master of this stuff, suspenseful drama. His works include Perfect Blue, Millenum Actress, Tokyo Godfathers, Paranoia Agent, and Paprika (new , haven't seen Paprika myself), all of which are highly recommended.
A new film that happens to be in Blockbuste ris 'Tekinkonkreet' (sp), which seems to be getting rave reviews.
I also moderate at Animenation.com (As Char), an anime discussion forum.
My most recommended anime has to be Gunbuster 1 and 2.