It depends on the game. Some games do that really well, and they end up being good. The ones with real stories are probably the best, in my opinion, but it depends on the game. Most of the time, FPS games that have elements of other genres are okay, as they aren't straight up Castle Wolfenstein clones. The really good ones end up being like Deus Ex: Human Revolution, in that they become very popular and successful. One example that comes to mind is the Half Life series of games. The story in them is amazing.
with a focus on combat and puzzle solving.