For me it depends mostly on the story length. If it's a novel or series of novels, I've invested a lot of time and I want a satisfying payoff. For that reason, I liked Return of the King (book and movie). If I've enjoyed it and there is no more to read, I want at least to be able to extrapolate what the sequel might be. "They lived happily ever after" suggests the monsters stopped coming around and they enjoyed the remainder of their lives in the little cottage. Maybe LoTR is not such a good example, because I gather Tolkien wanted to present it as part of a much bigger alternate history sort of thing, and real-world historical events rarely have a cut-and-dried resolution.
For short stories, it's not so important to me to know exactly what went on before and after. It's more of a mood thing. There may be no time for such luxuries. In many of Bradbury's short stories, it's the setting and mood that I remember years later, long after I've forgotten the characters, plot, and ending.
This is not to say that there are not short stories that need to tie up all loose ends, such as Sherlock Holmes stories ending with the revelation of the solution; or most of O'Henry's, where typically the last paragraph has the punch line. In such cases though, I suspect that the ending was often the first thing that the authors came up with, and they built the rest of the story around it, so "how to end it" was not an issue.
I'm still not sure how I feel about Stephen King's final installment in his Dark Tower series. Roland's part in it made me think "Oh crap, King's not going to ... yup, he's gone an done it. d'Oh!", and that King bailed out of writing a "proper" ending, but really I suppose it was resolved in a way that pretty much nails down "what happens next".