It's a hard say. I think everyone's best anime must fit their individual tastes. There's a couple animes that almost anyone can enjoy like Cowboy Bebop, Samurai Champloo, Rurouni Kenshin, GANTZ, Elfen Lied and Gankutsuou.
I personally enjoy psychology, philosophy and abstractness in my animes, so my absolute favorites are Evangelion, and Serial Experiments Lain. Paranoia Agent was also very good for that.
I suggest doing a little research. Use sites like
Anime Source and the
Anime Recommendation Database . See what people have rated as great, check out the plot on Wikipedia or something, and try them out for yourself.