Most webcams come with software to control them and you can use that software to take snaps with. We use two logitech webcams and they work fine, decent video output and the software lets you take pics too.
Snapshot what their camera is showing? How about a screen cap or something? Camera control is one way and only at the originating end I think.
This is the webcam I use and I've not had a problem with it since I got it.
linky