I might make some really big enemies in my first post on this website.
It all depends on what you consider a great anime. Code Geass had that rare ability to bring me to the point where I needed to see the next episode. I didn't want to put it down or take a break. It's very hard for me to find an ending I like. We can all think of a few epic failures to show endings (i.e. Evangelion, Death Note, Full Metal Alchemist, etc...), but Code Geass' ending was as close to perfect as I've ever seen. So in my opinion Code Geass wins the best anime in my book.
Cowboy Bebop fans, I'm sorry. That show = epic failure. It was an awesome idea. The show was just plain cool, but outside of that it has nothing. I own the whole series on DVD and have seen it twice after watching it with other friends. I can say that there are probably about 8 episodes that actually pertain or even hint at the plot, and each episode is almost a stand-alone episode. The only ones that weren't stand-alone were the last two or three, if that. Cowboy Bebop by far had the most potential but was awfully done in terms of plot.
A comparable one to Cowboy Bebop was Burst Angel, and i felt like wringing the makers of that anime by their necks after they butchered a show with such great graphics by using such a pitiful plotline.
