Many tables and chairs are sold cheaply because they wobble, and few people realize this can be an easy fix. Turning them over and looking at their construction is often the way to choose whether or not to purchase them for refurbishing. Those that have legs attached with screws are often the easiest to fix, so it is a good idea to investigate these pieces instead of passing them up for something more expensive.
Legs are designed to take the weight of any furniture piece, and those that are screwed or nailed onto the furniture loosen over time. Many of them may simply need new screws, and other pieces will only need a few turns of the existing screws to make the wobble go away. Refinishing the surface of the piece after that is generally a matter of choice for a hobbyist who wants a new looking piece of furniture.