Not all bikes shimmy. The reasons that Thylacine mention are the main reasons. But new ultralight bicycles that are welded also have a tendancy to experience this phenomena more than the older heavier lugged frames or touring bikes (comparing both welded and lugged to only mid and high end bikes). I use to race back in the mid 70's till mid 80's and no one I knew, or heard of, ever experience this phenomena and we all were on lugged steel frames. There could be problems with the newer paired spoke rims or low spoke rims that could also cause a problem as Thylacine also noted, except some LBS mechanics do not think this is a theory but could be a fact. When I was racing most guys raced on 32 spokes, some did 28 and some did 36; I ran 36 all the time I was racing.
You could also get a imbalance wheel and tire combination but those sort of shimmys are harmonic thus only occur at certain speeds (like only between 20 and 25) but will occur at that certain speed all the time until you correct it. This is the same thing that happens to a car tire.