Some people are truly gifted when it comes to diagnosing a car problem just by listening to its noises. For them, that little squeaking means the water pump is about to give up, and this weird clicking tells them the valves need adjustment.
For a lot of people though, these noises mean nothing, other than it is time to bring the car to a mechanic. There is a website that can help you: mycarmakesnoise.com. It is a very comprehensive sound bank, classified by categories: Engine compartment, under the car, front, rear, sides… You listen to the sounds, and compare them with how your car sounds! A lot of noises are recorded, from the simple whine of a belt to the dreadful sound of an oil-less engine seizing.
And for the smartphone generation, there is an an app for that! Named ClingClanger, it works the same as GrooveShark (or SoundHound): your phone will listen to the noises of your car, compare it with its database, and tell you what the problem is. It will also give you a list of possible broken parts, and tells you the severity of the problem.