Lethe, the thing is, I've watched a copy of the original TV release of Evangelion, and it blowd my mind the same way fans of SW were blowed away in 1977. So... I don't know, I feel like it's altering a masterpiece.
GundarkHunter unfortunally no, but I know that anime, and I think my brother has a copy, I'll ask him.
TheSessler: start with Evangelion, if possible the japanese DVD version - since there are two versions now, why not watch the "most complete" one? Gaaahh I feel dirty saying that, like GL is laughing and rubbing his hands somewhere. OK other animes you could watch:
If you like the goofy anime style, I recomend "All Porpouse Cultural Cat Girl Nuku Nuku", if possible the OVA, not the TV series. Also "Naruto" or "Ranma 1/2", which have relatively easy plots and are fun to watch.
If you are into something more adult, perhaps "Cowboy Bebop" if you like sci-fi and noir. If you enjoyed Matrix, perhaps "Serial Experiments Lain", althought I hated it. "Akira" and "Ghost in the Shell" are good movies.
If you wanna see some good old classics, I'd recomend any anime by Osamu Tezuka (but avoid anything produced after 1990), or "Yamato" (known in north america as Star Blazers) - I could recomend the movie "Yamato Final".