I think there are five aspects of an amazing ending. My favorite books have all five, some have two or three, and some (series in particular) may only have two. These are what I strive for whenever I write the conclusion to a story.
1. The Twist. A sudden reveal, an exposed secret....plot twists really help make the ending of a book interesting. Here I'd quote Harry Potter and the Sorcerer's Stone. When Harry walks into the room with the Mirror and sees Professor Quirrell instead of Professor Snape, it shocked most readers out of their seats. (Figuratively. Unless you actually did fall out of your seat, in which case literally.) It was the biggest OH SNAP moment of the book.
2. Physical Action. Let's face it, a climax would be boring if characters just stood around talking. Physical action is essential to move the plot along. In Philip Pullman's The Golden Compass, the climax involves an elaborate escape plan, the main character almost getting ripped in half by sadistic religious scientists (all Catholic-Inquisition-style), and blowing up a detainment building in the middle of Arctic nowhere. The physical action is very effective and well-paced.
3. Emotional Action. Every good main character should have an emotional journey. A climax needs to expand upon these emotions, and the character should face mental barriers as well as physical. I know opinions are divided over Mockingjay, the final book in the Hunger Games trilogy, but in terms of emotional impact the climax is perfect and moving. Katniss gives up everything to protect her sister Prim, but in the end she can't save her. It's a sad and dismal ending, to be sure (although the last chapter does give some hope for the future), but the emotional climax is far more effective than a climax merely based on action.
4. Resolution. Honestly, I'm not a huge fan of series in which books end on complete and total cliffhangers. I think, in order to create a good climax, there needs to be some measure of resolution. Again, I think the Harry Potter books are particularly good at this. They leave you salivating for the next installment, but every book contains its own individual story, and all the major points of these stories are wrapped up by the end of the book. They satisfy readers' curiosity as well as hinting at events in the next installment.
5. Unity. I think this is the hardest part of a climax to nail: combining physical action, emotional action, themes, etc into an ending that wraps up all (or most) loose threads. Authors who can come up with a climax in which a single event relates back to all these things (i.e., the character's emotional journey and physical journey come to culmination in one arresting moment) create the most satisfying and emotionally wrenching climaxes. Here I'd quote Ptolemy's Gate, the third and final volume of the Bartimaeus trilogy. Author Jonathan Stroud pulls off the absolute best climax and resolution I've ever read. For those of you who don't know, there are two main characters in the Bartimaeus Trilogy, and Stroud manages to converge both characters' emotional and physical journeys, as well as the book's overall themes, into a single final instant that's absolutely perfect in every way. Stories are made up of multiple threads, but the very best climaxes spin these threads together into a moment that can be used to summarize the book as a whole.
So there you have it. Those are five points that (in my opinion) contribute to an amazing climax. Do you guys like writing your own endings? Do you find them difficult, or easier than the beginning and middle? What do you think makes a good climax?