The second method is to use a camera that has a fairly wide field of view, and to tilt it at a fixed angle while rotating it around the pan axis with a servo. This is the idea behind the BEAK rig:
It looks down at a fixed angle, but rotates, taking pictures periodically so there is overlap for stitching panoramas. Or, in the case of Photosynth, so there is overlap for connecting the photos into a synth.
This approach is slightly more expensive than the first type, but not by much. Parts for a BEAK kit run about $80US, minus the kite, line, and camera. In terms of camera gear, it about on par with a good lightweight tripod. (To be fair the tripod I'm lusting after at the moment runs about $650, so my definition of "good" and "lightweight" may differ from that of others.)