Here is my list of the few animes that I have liked. For the most part, I saw them on Adult Swim, so I'm not sure if they are edited versions or not.
Cowboy Bebop: This one is absolutely awesome. Great work on the gun stuff. The final shootout where Spike assaults the syndicate HQ is magnificent.
Samurai Champloo: Another one from Shinichiro Watanabe. Nice road trip story around feudal Japan with lots of cool sword fights.
Blood+: Kind of hard to describe. Sort of reminds me of Highlander mixed with Blade. A mysterious girl, her bodyguard, and adoptive family fight to stop a long lived conspiracy of Vampires trying to take over the world.
Ghost in the Shell: Cyborg supercops work with a team of hackers to fight crime in a somewhat dystopian cyperpunk future.
Sword Art Online: I mentioned this one in the Internet Weirdness thread. I wouldn't recommend it unless you play MMO's, but it is interesting if you do. I thought the concept of a VR version of World of Warcraft where you can really die provided a good background for the story. Overall I would say it was good, but it has some annoying anime tropes that ultimately keep it from being great. You can skip the second half of the first season, that drags on and takes a turn for the creepy. It gets better again in Season 2.
Attack on Titan: Sure, the premise is somewhat preposterous, but it makes up for it in atmosphere and good production values.
Fate Zero: Been watching this one on Netflix, and I'm about 2/3 through. It is set during the late 1990's and covers the events of the "4th War for the Holy Grail". Every 60 years, 7 mages are selected to fight for the grail. They do this by summoning various legendary heroes (King Arthur, Alexander the Great, Gilgamesh, etc.) and with their own skills. It is somewhat violent, but like Cowboy Bebop, there is also some great gun action. One of the mages, Kiritsugu Emiya, actually bears a striking resemblance to Spike. He's not as talented at the magic stuff, but he makes up for it with technology and cunning. One interesting thing is that the story is somewhat interwoven between all the main characters. You can't exactly pick one to root for. They all have different goals and motivations. None of them are either completely good or evil, with the exception of one. He's a crazed serial killer that isn't interested in the battle at all, he only wants to cause death and destruction. He eventually gets taken out by the other teams when his servant (also an insane murderer) summons an Old One to attack the city. I heard this is actually a prequel to another series and movie that I haven't seen yet.
Knights of Sidonia: This one is a Netflix exclusive. Think Battlestar Galactica with giant robots instead of vipers, and crazy bio-organic space monsters instead of Cylons. Really liked the first season, but the second one declined drastically. The second one was nothing but a bunch of stupid relationship drama. Way too much of that crap, and not nearly enough giant robots shooting monsters.
Full Metal Alchemist: Two brothers with magical talent try to bring their mother back from the dead and it goes horribly wrong. They join the military and wander the land trying to find a way to undo some of the damage they caused and have various adventures along the way. Fairly good, but it does have some of the usual anime things I hate. It's fond of using the wacky comedy bits where the animation looks all weird. I hate that crap. There are also two different versions of this show. The original one came out when the source material was still being written, and then it drastically diverged. It was remade a few years later with a different story line that followed the events of the manga after the original diverged. I haven't seen that version.
I've heard a lot of people like Robotech, but I never saw it. I didn't have cable in the 1980's, and it was never syndicated here in Kansas when I was growing up. I did read the novelizations when I was in junior high and enjoyed them, but never saw the show they were based on.