A lot of those aren't anime, as has been stated
If you want a good one to try that isn't on your list already, may I suggest Code Geass? It's a personal favorite of mine.
You should also check out some of these;
The Melancholy of Haruhi Suzumiya (about a girl who loves strange things like ghosts, aliens, witches and time travelers... and ends up being friends with a few! A very well-balanced series. If you watch the second season though, you'll need quite a bit of patience. The first 7 episodes or so are almost exactly the same!)
Ouran Highschool Host Club (this one's about a girl who gets into a fancy school on a scholarship and while looking for a quiet place to read, stumbles upon the school's host club! ...And then accidentally breaks an expensive piece of pottery in their room and has to disguise herself as a boy and work as one of the hosts to pay it off. Chaos ensues!)
Lucky Star (if you check it out, it will be the most pointless and weird anime you will ever watch, but the comedy never ends! It was based off a 4-panel comic series, and there is no plot whatsoever, but that's kind of the point, anyway!)
Cowboy Bebop (if you liked Trigun, you'll like this one. It's a classic about space cowboys and smooth jazz!)
Rurouni Kenshin (another classic, this one's a somewhat historical story of a famous samurai who lived during Japan's edo period)
Samurai Deeper Kyo (see above description. It's about a medicine peddler who's actually a notorious samurai)
Darker Than Black (if you like Code Geass, you'll like. The concepts are pretty similar as they both contain weird eye powers, green-haired heroines, and numerous Pizza Hut ads)
Full Metal Alchemist (this series was so good, they made two animes of it! It's the tale of two brothers who tried to use alchemy to bring their mother back to life and failed, costing the older brother his arm and leg, and the younger brother his entire body. The series basically revolves around the brothers trying to find the philosopher's stone, which they can use to return their bodies to normal. The first anime followed the series until halfway through it, because the manga wasn't complete yet, so it branches off in a completely different direction. The second anime, Brotherhood, follows the manga almost exactly, with the edition of a filler episode here and there to make some time, and it moves much more quickly than the first anime.)
Quickly, here are a few more
Axis Powers Hetalia, which is a history-based comedy where the countries are personified
Batman Gotham Knight, which is, despite being about Batman, actually an anime! It's a great psychological-action-thriller take on the classic superhero
Any of the numerous movies directed by Hayao Miyazaki, which are all amazing. If you watch Ponyo, though, watch the Japanese dub and save yourself the pain of listening to the crappy English voiceovers which were done by actual 6 year-olds
Highschool of the Dead, which is a very new (new as in, it started in the summer of '10) anime about a zombie apocalypse. Very cutting-edge as far as animation goes.
As for anime movies, Akira is the best one around. It's the classic of classics, but the plot is incredibly dark and don't watch it if you have a weak stomach
Also, try Fist of the North Star, Great Teacher Onizuka, Rosario+Vampire, Sailor Moon (that's a long one), Fooly Cooly, Neon Genesis Evengalion, and Gurren Lagann
Whew, that was some list!