I'm riding my sister's old mountain bike, for the time being while I save up for a Specialized Allez double, and I noticed the other day that the back wheel felt to be loose. When I jiggle the handle bars the bike feels pretty loose. I rode home after going through some rough terrain by forced accident, nothing seemed to come apart or be bothered by it. I get back and see to tightening the bolts, maybe they loosened on me somehow. I tightened, spun the wheel and it still seemed to be wobbling back and forth a smidgen. I untightened, reset the wheel, and tightened again, no improvement. The air pressure is fine, since it's not my weight that's causing the wobble.
Perhaps I'm just paranoid and never noticed that it does slightly wobble by itself.

In case the brand maybe an issue, it's a Royce Union Mistic. It's chain has been recently lubed (with Prolink), which was the first time I've ever performed bike maintenance before.