Yeah, the first thing I'd check is the subframe mounts. I looked under my '96 a couple of weeks ago, and one of the big washers was just hanging there!
Further inspection revealed that another one was missing altogether. The bolts were there, but the washers had rusted out. Scary. All fixed now though.
Otherwise, the small animal theory seems reasonable. In this case, there is often evidence left behind in the form of fur, or sticky liquid residue, on the underside of the car. Sometimes the "Thump" is also accompanied by a "yelp", or "squeak".