Should I install Xbox 360 games to my hard drive?

One of the benefits would be that your disc will get less wear and tear. You still need to put the disc in, but after verifying it, it shouldn't be read again (though that will depend on the game). This should minimize the danger of scratching it if the console gets knocked. There should also be less noise as it doesn't need to keep the optical disk spinning.

You might also get faster loading times - but that would depend on the game.

An obvious downside is that you are going to fill your hard drive if you do this for all your games.

In general, you will get faster loading times reading from the hard drive than the disc. However, this is not always the case, especially with some of the older games.

One example is Halo 3. Don't install Halo 3 to your hard drive. It will actually perform worse than if it read off the disc (because the game was already made with caching from disc to hard drive). The reason for this behavior is because Halo 3 was released before installing games to the hard drive feature existed and therefore they programmed their own caching to the hard drive as a part of the game.

Looks like installing might allow you to play discs that are too damaged to play directly, which is a huge advantage in the right circumstances.

Can I verify an Xbox 360 game isn't damaged by installing it?