NOIR is the best anime. It's about these two female assasins, and a related organization calle Soldats, but the story is far deeper than you're average assasin story. I had this feeling that I was watching something important, something significant. Action sequences are awesome, and the subtleties are magnificent.The soundtracks are some of the best in all of anime. Kind of a mix between gregorian chants and techno/trance. Lots of tracks even have a hard rock edge.
Berserk is another anime completely and thouroughly amazing anime. Think Machiavelli when watching this, and pay attention to the setting that it's taking place in. Certain things hit me by surprise (even if the 1st ep let me know it was that type of anime, it wasn't apparent) and they were all good surprises. I really don't want to say too much about this anime, but if you like deep and involved stories that are actually easy to follow, and also animes that comment on the nature of man in general....then this is definately for you.
There's a myriad of other things like gundam wing, scryed, helsing, crest of stars, last exile, rahxephon, and evangelion. It's not a complete list, but they're some of my favorites. In the way anime movies, you should watch akira if you havent, street fighter the movie (I loooooooove fighting), fist of the north star (again with the fighting), and vampire hunter D (cuz vampires rule, and so do vampire hunters).
Comedy anime wise, I like gto, tenchi series and love hina (both romance comedy type things, both have some action too).
More recent good animes are Narutaru (don't be fooled by the cute little pokemon-like thinggies. extremely disturbing, you've been warned) and Full Metal Alchemist, which is actually still going.
If you actually watch all of these, you should get a good idea of the kind of anime you're into. Have fun.