This is probably the most common vibration people deal with. There’s an important distinction to be made with steering wheel vibrations. Does the vibration happen all the time while you're driving, or just when you step on the brakes? If it happens all the time, it's likely to be a tire or tire balance problem, especially if it occurs around the 55 to 60 mph range. It could also be a driveline issue, but the most common causes of this type of vibration involve the tires or tire balance.
If the vibration only happens when you step on the brakes, then the problem likely is the brakes. This does not necessarily mean that your brakes are about to fail, but rather the brake discs (or brake drums) have become out of round, or warped. When this happens and the brakes are applied, you get a vibration. You can deal with this vibration in one of two ways. You can have the brake parts machined true again, which should get rid of the vibration. Or, if the brake discs or brake drums don't have enough metal material left to be machined, they'll need to be replaced. Here's a video covering this topic in more detail.
As stated in the video, this test won't work for all vehicles. It depends on the type of parking brake setup you have. See the Brakes article for more details on this topic.