I've been thinking a lot about Jasper. I find him fascinating. Except for him telling his backstory to Bella in Eclipse, Jasper is almost never the focus of attention. He is the center of Alice's world, but no one else's.
In Twilight, Jasper seemed to exist so Alice had a mate. We understood that they were "adopted" into the Cullen family, and that Jasper was less comfortable in the "vegetarian" lifestyle than everyone else, but that was all. Even Bella's stay with him in Phoenix did little to illuminate his character; Bella herself states that he becomes distant and remote once the sojourn is over.
In New Moon, Jasper is absent for the majority of the book. However, Jasper is the catalyst for the entire story. His lack of control at Bella's party is the single act that precipitates everything that follows. If Jasper hadn't attacked her, would Edward have left? If Edward hadn't left, would he and Bella have stayed together? Jasper's loss of control was responsible, in my opinion, for the rest of the story.
In Eclipse, Jasper reveals himself to be hiding a great deal of strength and intelligence behind that quiet reserve. He manages to train vampires and werewolves together. He reveals that he is the member of the Cullen family with the most blood on his hands. He has slaughtered human and vampire alike for years with little remorse. Only the weight of hundreds of lives taken, and the example of his underling, makes him realize that the life he is leading doesn't make him happy.
In Breaking Dawn, Jasper becomes a figure of tragedy. In witnessing Bella's transformation, Jasper must realize that so much of his own behavior is a result of his own choices, not the implacable will of nature. He is absent again, for much of the novel, when Alice leaves the family, and when they return it is Alice's triumph, not his. No one misses Jasper. No one is shocked that Jasper left. It is Alice they love and miss, not him. But he does return, and when he does, we have the satisfaction of seeing how happy he is with his family.
His relationship with Alice, along with Carlisle and Esme's, is one dealt with in almost purely emotional terms. We don't get references to them being physically intimate, though I'm sure they are. What we do get from them is the idea that they love each other to the exclusion of everything else.
What do you think about Jasper?