I am not a tremendous anime fan myself, but I have found these to be really well written and animated:
- FullMetal Alchemist Brotherhood - probably my favorite one (I think it is also more in line with the manga, which is usually good)
- Neon Genesis Evangelion (complicated neo-theology based story that I liked)
- Evangelion 2.0 (which you could argue falls in the previous one)
- Darker than Black (just started it a few days ago, loving it so far)
- Death Note (goes without saying)
- D. Gray Man (enjoyable while being lacking at times)
Entertainment-wise I like (please don't hurt me) :
- Great Teacher Onizuka
- Bleach (sans the fillers, the bount arc made me cry in pain, I had to skip some episodes) it is good fun though, and became really interesting when the Arrancar arc started (its not the best, I just like it for easy entertainment)
I think Ichiban Ushiro No Daimaou could have been a really good one had it not focused so much on partial nudity to "sell". The story was also rushed into 12 episodes and it felt as if they skipped to the end... They don't explain a lot.
Again, not a huge anime connoisseur.