Greg Egan's Permutation City is a story that takes a pretty interesting approach (and, trying to not give away too much, extreme perspective) to this question. I would stop short of glowingly recommending it because I found the storytelling itself to be only okay, but the core idea and take on this matter itself was one of the most memorable concepts I've seen in hard scifi.
Permutation City is the most fresh and insightful view on consciousness I have ever read. Every page is mindblow after mindblow of ideas you thought you knew but have never seen them taken to those consequences. I look at computer science as a beautiful philosophical minefield of interesting takes on language, existence and consciousness, and Greg Egan is a huge part of that. I never found someone who writes like him.
IMO, Greg Egan is one of the greatest geniuses I've ever come across, and I strongly recommend his novels and stories ... but I think it's worth noting that he's said that he doesn't believe that the theory of consciousness that Permutation City is based on can be true.
