I just recently noticed this noise today. It's just a random little squeak that sometimes happens with a bump in the road or turning, and sometimes if I brake a little hard. I drive a lot for my job and I would like to figure this out before it becomes more than an annoying little noise.
Oh... There are just _so_ many things that could cause that. Many innocuous, most leading to parts needing to be replaced or at least serviced at some point.
I'm sure others with more experience will chime in, but it can be the following.
Shocks/struts going bad. It happens. You can _usually_ repeat this by parking on a flat surface, and shaking the car. Shove from the driver fender towards the passenger side. Then repeat from passenger side. From the top, jump and put force downward on the top of the fender, both sides. (You're trying to compress the spring and shock slightly. The shaking back and forth is for the mounts)
Brakes needing to be serviced. (This is possibly the cheapest thing, but with it happening at a bump, not very likely). The brake pads move in channels. Most people put channel clips which are chromed steel into the cast channels. They can wear, and they _can_ rust. So eventually the metal starts squeaking when the lubrication gives out. Usually this is when you push on your breaks, and your hear a squeak. (Can also be caliper slide bolts, piston, etc)
Ball joint and tie rod ends. Jack up the tire, and jerk it from side to side. Then top to bottom. If it wiggles, you have issues.
We'd need to know more about the car to give better information.
1) Where do you reside? (fill out the profile).
2) How many miles on the car?
3) Which car do you have? Year, trimline, transmission type?
How thick are your brake pads? The wear clips for thin brake pads will make noise mostly when you apply the brakes but if the pad does not retract away from the rotor, you may get random noise from them. Also do the things Bookworm said and report back your findings so the trouble shooting can continue.