Yeah I consider Thundercats more American Anime, if there's even a classification for it. I agree with you however, that a lot of what's coming out is crap, probably because they think that it's a cartoon, and think it should be made for children, thus short plots with a simple story, with some goofy slaptic and corny phrases... what a mess.
I like Anime because it's the complete opposite of American cartoons. The stories are actually better; they're more involved. One thing I love is character development. A character learns throughout the entire series and looks back on what he's learned. Also, many deal with real life issues. Not everything is about little monsters that shoot out fire. That's just the story. There are also no restrictions. Just because its like a cartoon (I even hate relating that word to Anime) it doesn't have to be PG. It does whatever it needs to do to get it's point across, whether is showing blood or scenes that portray sex, just like a R rated movie. I have to add that most of best movies I've seen have NOT been rated G or PG13. The art is another thing all together.
Most of the time, the artwork is a lot better. I think many of you can agree on that. The music is also better I think. Most series have their own soundtrack with usually more than one soundtrack (Initial D has over 8 soundtrack CDs I think).
Just my thoughts on Anime. The current Anime I'm watching now is Chobits and Hajime No Ippo. I think my favorite Anime though, the one I've enjoyed the most has been Initial D still.