There are a few pieces of software out there that will do what you're looking for. I'll leave the hardware debates to others. (I personally own a Hauppauge WinTV+radio)
Cinax has a handy little program called
WinVCR that has been out for a while now. Incredibly easy to use, it will capture video as either MPEG-1 or Microsoft's ASF. I've used the demo a few times and like it. I might even buy it at some point in time. Check it out
here.
Showshifter also has a product that recently came to my attention that
almost mirrors the TiVo perfectly. In function, at least.
ShowShifter is currently in
beta, but looks rather promising. It uses the
free MJPEG codec as its primary compression method. From what I've read however, it will also support any other codec installed on your computer. Including
DiVX ;-), thankfully. I haven't tried it yet, as it looks like it is an
adware based program. I'll try it out on my Win98 partition and let you know what I think of it. There is a
free beta available to download if you want to try it out on your own.
If you end up getting a Hauppauge card, included with the driver software is the program that I prefer,
VidCap32. Incredibly small, direct and to the point, it utilizes any video codec installed on your computer. My only complaint is that I haven't figured out how to use other
audio codecs in it yet. That could simply be my own problem though. It's
free though, so what can you expect?
Enjoy!