@Superevil225: I do like some of the older ones, such as Evangelion, which is another great one, but between the budget cuts and the numerous re-imaginings with the ending, I find it tough tough to really understand what's going on. FLCL left me with questions that could easily be answered by just watching the 6 episodes (3 hours) again (maybe even a 10th time) where as Evangelion left me with questions that may never be answered.
FLCL is great but not greatest in any shape of the imagination. This is because no matter how great the art and music was, how funny the off the wall comedy combined with the classic 'coming of the age' story is, it doesn't change the fact that its only 6 episodes long. 6 episodes of awesome-ness yes, but by the time you get into it, its over. Even my favorite anime (Evangelion) I wouldn't class as the best. I personally don't think the best anime has came around yet and maybe it will never will. Or maybe it'll just slip under the radar. The closest I would say is Angel Beats! just because its funny, has a great story line, engaging characters, it isn't dragged on but isn't too short and it was the first anime that made me cry X D The greatest anime (in my opinion) will appeal to many audiences and I just don't think FLCL (or Evangelion for that matter) does that.