I was watching anime before it was "cool", when I was but a wee lad.
Speed Racer, all the old robot shows such as Steel Jegg(?) or Mazinger, etc, are for all intents and purposes, anime. Of course, they are continuity free, saturday morning cartoons. And of course Macross (bundled in that Robotech thingy. someday I'll get the original)
I've seen a lot of modern anime. These are my opinions:
-Akira: very visceral, kinda interesting. I really hate how everyone's heads look like those Lego guys (the author usually draws like that in all his shows).
-Evangelion: this is a anime that takes the most mundane and boring story and tries to turn it into some kind of deep philosophical mumbo jumbo, with Wangst everywhere at every single second. Whenever Lil' Whiny Boy starts crying, or Tomboy Angry Bitch starts being mean for no reason at all, I feel like kicking both of them in the face.
-Cowboy Bebop: this show is pretty damn awesome. Jazz music, the 70's in Space, unconventional sci-fi physics, and lots of high kicks to the head. I don't care much for the ending. I also don't care much about there being a "prequel" movie to that ending - I hate prequels. If watched before the final episode tho, it's also very cool.
-Gantz: this show is all about the gore. It's very annoying. There's almost no plot: literally, the plot is: we have no idea about what the fuck is going on and we're all gonna die gruesomely. Oh and everything is so mysterious (because the author has no idea what he's gonna write next). I saw the entire anime, I heard the manga is much better, but the premise is the same - dying and having no idea why.
-Card collector/monster dueling animes: yuck...
I have seen more but I don't have strong opinions about most others.