I'm not sure it's as simple as that. If it were, there'd be a lot less fire and brimstone issuing from Southern Baptist pulpits...hehe...
I can't speak to many other denominations, not being as familiar with them as my own, but here's the Lutheran point of view. Given Original Sin (the eating of the forbidden fruit in Eden, and the following consequences), we, as human beings, can never be "perfect", no matter how hard we try (the strongest case against Christian smugness, by the way, in case you ever needed one). Therefore we can never "earn" or "deserve" salvation. Rather, it is given by God to those who believe in him, because he loves us.
Now, if we are in that relationship, we cannot help but do works - where works can also mean a lot of things, but generally are done in the service of God, either directly, or by helping others. But this is not what saves us.
In a way, there's a fairness to that. Critics like to go directly to the worst case scenario - the monster that repents on their deathbed. I'm not sure about that...I've sent the question out, will let you know the response. (My mother is a Lutheran minister, so I have a nice "Call a Friend" lifeline options...hehe) But from a more practical standpoint, works based salvation is actually rather ableist. Does a person who cannot perform works due to disability not get to go to Heaven, despite their great faith? (Rhetorical question, since no one really knows, beyond what the Bible says, and look how many ways that gets interpreted).
Bear in mind I'm not arguing correctness, I am simply sharing Lutheran ideology. Every denomination will have their own specific ideology on this, with most landing in a tight grouping, and a few others who find themselves a little on their own. In the end I believe it all amounts to the same thing...with the difference being how we view each other. A faith only denomination will look at a faith+works denomination, see their faith, and say they are saved, irrespective of their works (which, of course, we'd commend them for). I'm not sure what a faith+works denomination would say about us, but that's not really a concern for me beyond academic interest. If it were, I'd probably belong to their denomination, not mine.
