Mance Rayder is still alive in the books, kind of, despite being burned alive on the show. Well, he's mostly alive. He was still burned at the stake.

In the book "A Dance with Dragons" and in season five of the show, Mance Rayder is burned alive at the stake. But, in the book, Melisandre does some red-priestess magic to switch Mance Rayder and the Lord of Bones' (aka Rattleshirt's) body. You remember the Lord of Bones, right? He wore... bones... lots of them. Anyways, Stannis wanted to burn Mance Rayder, but Melisandre thought Mance Rayder would still be useful later on, so she wanted to keep his soul alive. She clearly didn't share the same thoughts about the Lord of Bones. It's really quite complicated and you should read "A Dance with Dragons" to get a full description of it but for right now: Mance = alive, Rattleshirt = dead.