I think the most common is people doing anything within the ruleset to win. And that's because that's what you're supposed to do and what both fighters signed up for. It'd probably be a sign of disrespect to do anything less. However, fighters still do care for other fighters safety. Probably the best example I have it the end of Teixeira vs. Saint Preux where Saint Preux goes unconscious by Teixeira's hand. However, Teixeira is unaware it happened, and instead of parading around the octagon, ends up checking out Saint Preux. Other sort of examples would be Joe Lauzon and Mark Hunt who try to finish the fight, but stop when they know its over, even if the ref hasn't.

But, there are tons of fighters who really don't care about the well being of their opponent. Jon Jones is one, where he'll eye poke you just to keep you at range. Blatant rule violations, ridiculously hazardous to your vision, he doesn't care. Anything to win. Other times they'll hold on to submissions too long trying to win. Some people would like to use Palhares as an example here, although I think he's just generally mentally unstable (he actually stopped one of his fights too early once and the ref was like "no buddy its still on"). I have to wonder if he really knows what's going on a lot of the time.

Then there's fighters who are usually A, but when you get in an intense rivalry they don't care for that opponent so much.

Finally there's others who probably just don't consider it. They go until the ref stops it and that's that.