It's difficult to determine exactly what happens to Seth McFarlane's foul-mouthed jumbo teddy bear at the climax of Ted and whether or not Ted actually dies. After a dramatic chase that ends at the top of Fenway Stadium's famous outfield wall the Green Monster, the teddy bear is ripped completely in half. It appears that despite John and Lori's best efforts to repair him, Ted does in fact die.
However, it's never explicitly stated in the movie, and given the magical nature of Ted's very existence and his return in the morning, it's tough to determine if he was ever truly dead. The real answer is a bit complicated, as the first question that needs to be answered is whether Ted is ever truly alive – a point that is thoroughly discussed in the sequel, Ted 2. The answer is further complicated by the fact that Ted is able to return to life the next morning, with all of his memories and personality completely intact.
Ted Does Die in Ted (Sort Of)
While still alive after the fall that results in him losing his bottom half and most of his stuffing, once the magic drains from his body Ted is, in fact, dead. That declaration insinuates that Ted meets all the qualifications to be alive in the first place. Morgan Freeman's high-powered lawyer Patrick Meighan states in Ted 2 that since Ted displays self-awareness, an ability to understand complex emotions, and a capacity for empathy, he is as much a person as any other human, given that these are the basis of what many would call a soul.
When the magic leaves Ted's body on the field at Fenway, he loses all of those abilities and returns to being a normal teddy bear. If a person is considered dead when everything that makes them who they are leaves their physical body, then it's pretty clear that the magic leaving Ted is as close a comparison as there can be. The fact that Ted is not "fixed" when Lori and John put his stuffing back in and sew him up proves that it isn't the body breaking that makes him dead – it's the magic leaving.
How Ted Comes Back to Life
As further proof of his mortality, Ted would have stayed dead had it not been for Mila Kunis' character Lori wishing him back to life. It took a wish from John to bring him to life 27 years before the events of the movie, and it took a similar wish to resurrect him after he was torn in half. While the audience never hears what Lori's wish was precisely, it's safe to assume that when she says that she wished for her own life back, it included Ted returning exactly as he was before he died.
Ted's origin and resurrection both raise a lot of questions about how the magic of the Ted universe works. For example, would a similar wish work on any inanimate object, or does it need to be something with a body and face like a teddy bear? It's possible that Seth McFarlane's upcoming Ted prequel series on Peacock answers some of those questions.