Cowboy Bebop is a very, very good anime, no doubt about it. The characters, plot, emotion, music, animation, action, and everything all combine to create an amazing experience. My only gripe is that it was too short...26 episodes isn't enough. The sad ending didn't bug me - it suited the show perfectly. One of the few times I've ever cried from some form of entertainment...yes, I admit it. The only thing that bugs me is the <SPOILER> relationship between Spike and Julia, and how it was so short-lived (yes, I know that they know each other from before, but they could have had her a bit more in the other episodes)</SPOILER>.
Trigun is very, very good as well, though the animation isn't so great, mostly because of it's age (about 1993, if I remember correctly). The show is funny, but it actually gets very serious once you get to around episode 15...and the final seven or so episodes are in some ways even more serious than Cowboy Bebop's. The plot of the show is very good, and it has some excellent twists and turns. You have to really watch everything. Once you get past the first ten or so episodes, things really start to pick up, even though the change is abrupt. Really, watch the whole thing, you will not regret it.