If you are talkin about YOUR webcam, it depends on your webcam whether it allows you to "record" what it sees. If it does allow, then, yes, a program associated with your webcam may allow you to choose the quality of the recording, format, and directory (which folder on your computer the recordings should be saved).
If you are talkin about pictures you see from some else's camera, most likely no, however, you can use a screen recording program (most commonly used to create computer tutorial videos, e.g. Riverpast, Fox Magic Screen Virtuoso just to name a few) to record what you see through the other side's camera.
