It's official, I am now completely hooked on anime. It basically all started this past year, mainly through access to Kazaaa and has just kind of snowballed from there. I was trying to explain to my friends just how good anime is (most can't get past the fact that it's an animation) when I realised just how much anime I've watched recently.
I think the first anime I saw was Castle in the Sky, but this was back when I was pretty young and didn't even realise the characters were Japanese. So that doesn't really count - the first time I knowingly watched anime was when I saw Akira, which to be honest I thought was good but the ending was a bit too weird for me. I didn't quite get it. If only I knew how often this happened....
I think my interest started from watching kung-fu movies... notably old Jet Li movies, such as Once Upon a Time in China (have you noticed they're releasing a film called One Upon a Time in Mexico) and Fist of Legend. Then my room-mate showed me Ninja Scroll. At about the same time, I half-watched Princess Mononoke whilst playing a game at my girlfriend's place, but even then I didn't quite get it.
I think the clincher was when I watched Spirited Away and it blew my mind. I was amazed at basically, how good it could be and how anime would always be able to convey images in a way CGI never could. And from there it just exploded... At first I just watched the movies: Perfect Blue, Ghost in the Shell, Visions of Escaflowne, Spriggan, Kite, Cowboy Bebop.
Then I realised that I was missing out on the true nature of anime; the series (of course the real true nature are the comics... but I'm not quite there yet). So I decided to check out Cowboy Bebop cos I had had no real idea what the dealw as when I watched the movie. Once again; blown. away.
Since then I've racked up:
Cowboy Bebop: A classic, one of the best, a ship of bounty hunters trying to earn a living, each one living with a past that haunts them and cannot be avoided. Great storyline that builds to a climactic finale. Very funky animation and soundtrack.
Neon Geneseis Evangelion: Another classic - some say the greatest ever. It follows one boy's quest for internal discovery as he is forced to pilot a giant robot to defend the planet from a series of mysterious invaders called Angels. Very deep - the ending to the series is very abrupt and badly done. Te movie End of Evangelion explains it better but is still highly confusing.
Outlaw Star: V. similar to Cowboy Bebop in style but with a more straightforward storyline but less funky.
Serial Experiments Lain: Woah! Major head-fuck alert! It's about a girl's quest for identity and why there appears to be a version of herself in the online world. Excellent, but is very deep, no real comic moments.
FLCL: I've talked about this before - weird, wacky and wonderful. One of the best - but maybe only appreciable after you've watched a few others
Berserk: Blood and guts galore as Gatts fights his way through thousands of enemies as he searches for meaning in his life. Slightly different format where it forms a continual storyline rather than separate adventures along a common theme. Very strong characters, good plot, the ending once again is very very bizarre and may disappoint.
Trigun: Follows the adventures of a wanted gunman who leaves a destruction in his wake and yet he refuses to kill anyone. Great series, hilarious in parts with a plot that slowly unwinds itself - it's a little lightweight, but good nonetheless.
Macross Plus: another classic. Amazing animation (the dogfight scenes are incredible). Strong story and characters - available in movie format as well.
Tenchi Muyo: has all the markings of another great series - a boy once more on a quest to find out who he really is whilst surrounded by 3 women, all of whom are interested in him (no, it's not hentai). The little rivalries and inter-character action is what makes it great.