I don't have the old anime experience of some people, but I have watched a bit of Pokemon, and the 1st and 2nd season of Digimon. I liked them both, I don't really consider them anime, more kid stuff.
For adult anime's I've watched Naruto, Inuyasha, Death Note, Full Metal Alchemist, Code Geass, and much of S-Cry-Ed. I've also watched He is My Master, Trigun, Read or Die, and Van Hellsing. Of them, I consider Naruto to be the best. It has the deepest plot, MUCH more human characters, and has the most realistic super-powers. I don't like Shippuden as much, and the filler was a tad disappointing, but of the anime listed here, I consider it the best.