Okay here goes:
Gurren Laggann. It gets to be over the top, but you should definitely watch it anyway. Make this the exception to your "out there" rule. The theme of perseverance in the face of adversity is so well done that Gurren Laggan should be required watching for the entire human race. It's only 27 episodes, but the ending doesn't feel rushed or anything (the show was made to be 27 episodes long, so the story is complete). There aren't any unanswered questions, and the pacing of the story is really well done. It is so epic, you can find the whole thing on youtube, legally and for free. A disclaimer though, episode 4 was done by a guest animator; it was a one-time thing and the series went back to its regularly good quality after that. Also, don't quit watching the series after the events of episode 8, only the weak do that. And they're missing out big time.
I am surprised at this, but it appears that no one has yet said Spice and Wolf. There are some fantasy elements, but the show doesn't emphasize them and the story and dynamic between the characters is really well done. There are currently 2 seasons out, and they are 13 episodes each.
Fullmetal Alchemist:Brotherhood. I doubt I can say anything that hasn't already been said much better. Definitely watch. It's 63 to 64 episodes, but they are all good. (All that I've watched anyway, I've missed a few here and there.)
Cowboy Bebop. Well done characters, well done story, the show has an interesting feel that is hard to put into words. It is a good feel though. It is very unique. It is 25 episodes if I remember correctly, maybe 26.
All of these anime have really well done English dubs (though there will always be some fans who think anime is always better in Japanese, even if the creator of the series himself prefers the series' English voice cast, as is the case with Cowboy Bebop). All of them have really good animation quality too, though Cowboy Bebop looks a little dated on account of it being so old. It's classic though.
As for Western animation, I would recommend Samurai Jack, Batman:The Animated Series, Young Justice, and watching Avatar again (I've seen the series at least 4 times, I love it so much). If you want some really good news, there is a sequel series to Avatar called The Last Airbender:The Legend of Korra coming out eventually. There is a trailer for it online. It is being made by the same people, so you know the series is in good hands.
I'm sure there are other series that fit your tastes I haven't thought of, but hopefully these will tide you over for now.