Surprised nobody's mentioned this one so I'll pop it in:
Bartender - While it's not exactly a show you might expect, I'd almost call it a history show in anime.. It's only 11 episodes long, but I liked the simple development and various educational material within.
Code Geass - I'd pick this over Death Note personally, as mentioned before the latest story arc in DN kinda shot it to hell quality wise, the first part was brilliant. Geass on the other hand seems to be going strongly, looking forward to where this one's going.
Akira - While I didn't like it that much personally, it's still a solid oldskool anime that kickstarted the sci-fi anime area.
Tokyo Godfathers - Genius little movie, highly recommended for laughs, character development, and plot movement, it's just damn well refined. For those who tend to read a little deeper, it does address many contemporary issues regarding the social state of Japan and the homeless.
Anything Ghibli - duh, or at least by Hayao. Tales of Earthsea I havn't seen yet, although I did read an interview with Goro and LeQuin, I hear she didn't exactly fall in love with the movie so perhaps there were some adaptation errors. I still plan on seeing it sometime just to see how his first film went though.
Full Metal Alchemist - Just because it's genius. I know people may think this one overrated, but I personally don't think I've seen a show with the character and plot development so brilliantly well integrated and executed for quite some time, and even makes you contemplate some things in the metaphysical.
Full Metal Panic - avoid The Second Raid if you don't want to see the original action and humour soiled by overly emo scenes. Fumoffu is mainly for laughs, treat it as a bonus from the creators.
Planetes - An *amazing* little series that hardly nobody knows of; it's a story in the near future where preliminary space travel to our nearby planets brings about many questions regarding the state of humanity and what our longer term priorities need to be, great food for thought. Again, character and plot are amazingly well done.
Slam Dunk - Just because. I'm probably biased for this one since it was one of the first mangas and animes I saw and thought it was hilarious, mainly for laughs, otherwise a little development and the rest is DBZ.
I think everything else has been mentioned...