I am not a lawyer and this is not legal advice. These are things I’ve heard many times over and have no reason to doubt.
Game mechanics cannot be copyrighted or protected in any fashion.
I could make a game called “Crystallized” that was Bejeweled, in every imaginable way, and as long as I didn’t copy the art from Bejeweled (either directly, or by drawing new art that just happens to be nigh-identical) I’d be totally fine.
Game mechanics have been copied often enough that, if this weren’t the case, I have no doubt we’d have heard about it by now. Game design is pretty much one giant incestuous ball of borrowing, and, honestly, is better for it.
Keep in mind that you can be sued for anything, even if you’re not breaking any contracts or laws, and they might win. But I’ve never heard of that happening with regards to game design.
Other answers have covered trademarks and copyright pretty well, but do not forget patents. Many game mechanics developed in the early days of gaming are patented. The 2 that I know of are minigames while the main game loads (Ridge Racer), and jump-in multiplayer (Gauntlet). That is why you almost never see these features in any games, even though they are both great ideas. In theory if you want to use these mechanics then you have to pay a royalty to the patent holder, which could be expensive. In practice however, it is very unlikely to be enforced unless you are making a million-dollar type game.
Game mechanics are not subject to intellectual property controls. Names can be trademarked and any game code or assets are subject to copyright protection. There is some legal precedent for going after games that are “close” (http://en.wikipedia.org/wiki/Lexulous) but that was in an Indian court so I know much less about their IP laws (see also: the various FOSS StarCraft clone projects, most threatened with suits because they had “craft” in the name).
Trademark law generally draws a distinction based on if an “average consumer” could be mislead into thinking you were related to the other property. Copyright is much simpler since it only covers concrete works. If you redrew every sprite from your favorite game they would not be violating any copyrights (but might be violating a trademark if it is something high profile).
Recently some companies have tried to bring patent suits against some big-name game companies, claiming things as outlandish as they have a patent for the concept of text chat. Time will tell as to if these are a real threat, but until your revenue is in the millions I wouldn’t worry about it.