I usually try to. On replays, not all the time (unless I REALLY love the game and haven't memorized what's about to happen, or just want to play)
I usually WANT to get into the story, but in some games I just can't stand it, and just want to play. This is why I'm afraid to start Devil May Cry 4, just like Bayonetta (I know that's playing them in opposite order of release), the cutscenes in DM4 I've heard are like Bay, and you watch awesome fights thinking, "I wish I could be having this much fun"
Cutscenes in games like God of War I think are the best, sure you can't skip them, but their tale is epic enough for me to WANT to watch them. RE4 lost it's charm after about the 7th time. It depends on the content, since cutscenes should explain the story, not play the game for you.