SharpCap supports almost all Webcams as long as you can find a Windows driver for the camera. In addition it supports most USB frame grabbers that are used to capture images from analogue cameras.
Most basic capture applications, such as AmCap and similar programs require the camera to be restarted completely when moving between preview and capture mode. This can be a problem for modern webcams as the restart may through away camera settings that you have just adjusted by re-initializing the camera back to an 'auto' state. SharpCap can move between preview and capture mode without needing to stop and restart the camera, which sidesteps this problem completely, as well as allowing captures to start more quickly.
Additionally, SharpCap allows the images being captured from a webcam to be processed by all of it's sophisticated features available to dedicated Astro cam users - for instance Live Stacking and Polar Alignment are both usable with images coming from a webcam or frame grabber providing that a long enough exposure can be set to start seeing details and/or stars.