What is the best way to get rid of scratches in the paint of a car?

Auto shops sell small bottles of touch up paint that are easily matched to the most popular car colors so you can fix it up yourself. These usually have a gloss mixed into it so they match the glossy overcoat on your car. If you have the money, auto painters can just touch up certain spots for far less than a full paint job.
If you don't feel like spending the money for either, but don't want to risk rusting (for when the scratch goes through the primer down to the body itself), you can just clean off the scratched area, and cover it with a few coats of clear nail polish.
Check to make sure it's actually a scratch too - sometimes what appears to be a scratch is just the paint that's rubbed off of whatever has brushed up against the car. In this case you can just use an auto cleanser, and lots of elbow grease!

They sell kits that kinda scratch off surrounding paint and re-glue it back to the surface.