Fullmetal Alchemist and its movie are both excellent, though, even though they it's vastly different from the source (and of course, the more faithful adaption in Fullmetal Alchemist: Brotherhood).

I think the Lord of the Rings trilogy is also quite good, even though it does stray quite a bit from the books, omissions aside.

It's really hard to make good media and I haven't found any reliable indicators hinting at whether an adaptation will be good or not. I found The Hobbit trilogy to be laborious despite having Peter Jackson at the helm of it as well. Though in that case, maybe the source material itself is the issue.