Obviously, endings are important. Writing style, character development, plot...that's what makes me enjoy a book as I am reading it. That's what makes me pick it up again and again, although there would clearly be other things I should focus on. They make me come back to the book as long as it is still on my nightstand.
The ending only gets important as soon as I finished the book - and usually way after I reviewed it.
Einstein once said, though, that knowledge is what stays in your head after you forgot about everything else (or, you know...something like that) and that's how I feel about endings, too.
Let's take Lauren Oliver and her Delirium trilogy, she was the first to come into my mind thinking about this topic. She is famous for making her endings the delicious part of the book, the big showdown that you are actually hoping for in every novel - but that you only get very rarely. Oliver understands how to create an amazing amount of suspense, how to kind of and somewhat satisfy the reader, but to still let so many questions unanswered that it's totally okay to complain about a cliffhanger. For Oliver, that works out. In some other cases, I'll admit, it doesn't, but that's a whole other topic.
Someone else who creates fantastic endings is Richelle Mead in her Vampire Academy Series. In the way she does it, she always reminds me of JK Rowling. All the books I've read so far have had big dramatic scenes in the end, but I never felt like there were just a few pages left out to make me excited about the next book. Mead always delivers a story that can be read by itself, which I admittedly like a lot better than Oliver's cliffhangers.
Similar to Mead's endings are both, the ones we find (or found) in the Caster Chronicles Series and the ones Marissa Meyer creates in her Lunar Chronicles. There, too, we always get one story with one purpose and one ending and if we want to, we can pick up the next book and dive into the story world all over again.
The queen of cliffhanger (really?) endings is probably Sara Shepard. Pretty Little Liars and The Lying Game books usually end with the mystery kind of figured out...and then the next book comes around and we are confronted with a whole new problem all over again.
Another good ending was Partials by Dan Wells - a huge book with such a story to tell - but if it weren't for those last few sentences I would have considered it a standalone novel. The ending itself was epic in several ways. There were action scenes, but also very emotional ones and some major decisions that I did not expect.
Although I'm usually very petty about cliffhangers, for some reason I really liked the ones Julie Cross put in her novels Tempest and Vortex - because they were so unexpected and they made me crave the next books in the series so much.
Lastly, I always enjoy the happy endings in contemporary novels - if they are done the right way. It should not be too easy for the characters to solve their problems, but I like to see them develop a whole lot (after all, that's what contemporary is about, right?) and grow and if they go toward a bright future at the end of the novel, that gives me a warm feeling of satisfaction :) Good examples for that are Katie McGarry's Pushing the Limits (of course) and almost every Sarah Dessen book.