Certainly. Many webcams come with motion detection and recording software of some sort.  Check the specs.

MPEG video compression actually works by recording just the parts of a picture that are changing - so adding motion detection isn't that hard for them to do.

Ideally you want the system set up to email video clips off site. Otherwise if the crook steals the computer he takes the evidence as well.

See this story..

http://news.bbc.co.uk/1/hi/england/cambridgeshire/4272041.stm

One thing to note is that the quality of the picture recorded is sometimes pretty poor when using cheap webcams in poor lighting. The system in that news article above used a video camera not a web cam.  Try a cheap webcam and see what happens.  Googling will find you clips from other peoples cameras so you can see what's possible with specific cameras. If the results aren't good enough try pointing the camera directly at the doorway.

You could also use something like this PIR camera that records movement onto a SD card...
http://www.spycatcheronline.co.uk/memory-camera-p-334.html

cheers guys

zam that looks great but a bit expensive for what i want to do

londonman it doesnt seem a very good review for that dlink

how much you looking for inc p&p??

Read the review. Depends on his definition of 'I know a lot about computers'.  Clearly he didn't!  It is capable of doing an awful lot and is streets ahead of a puny webcam. For example as long as you have an internet connection (and it can be wireless) you can view your camera from anywhere in the world and from any PC.  You don't need a PC at home either as it has a webserver built into it. It can send pictures to an email address plus loads more. But may be overkill for what you want to do.