I am looking for a list of at least two softwares (freeware,
shareware, or full-featured time-limited demo) which will watch the
images from a web cam and every minute or so grab it and save it on my
hard disk, then assemble it into a moving image gallery. I have a web
cam in a remote location, and I'm looking to create a visual log of
what it recorded through a day.

There are several shareware programs available to suit your needs,
assuming you are using some form of windows. They offer varying
features, but all will enable you to download webcam images from a
specified url
at a user-defined time interval:

1)CamCollect- http://www.rocketdownload.com/details/inte/3707.htm
Shareware
2)NetroCam- http://www.netrocam.com/ Shareware
3)Web Cam Mania!- http://www.seacoastlife.com/webcams/ Shareware
4)tkCamGrab 1.07- http://www.terrik.com/tkCamGrab.shtml Shareware

Hope this helps!