ATI Radeon 2400 or 2600HD in AGP. That will support HD decoding natively, so you can pull HD over the air (hey Indy, OPB, etc are still nice to watch in HD occasionally) or more easily watch downloaded/recorded HD shows. Just requires a DVI or HDMI capable screen (basically a decent HD TV or LCD monitor and appropriate cables) For non-HD content (most TV and movies) it has S-video out as well.
To turn it into a TV receiver you'll need a TV tuner card. Hauppauge and ATI both make good TV tuner cards, I would lean towards one that has HD capability and comes with a remote. If you're using Windows, get the MCE version of the tuner product as the generic remotes under Windows aren't as functional.
Operating systems:
Linux is a great solution but more time consuming to get working with some of the components, but can run on slightly lower end systems. If you're not comfy with Linux or have no interest in becoming so then stay with the Redmond bunch.
Windows XP Home/Professional: There is a limit to the number of DVB tuner cards that can be used at once. (I believe that it is limited to one DVB card with no limit on Analog tuners although the issue may have been fixed in SP3)
Windows XP Media Center Edition: Early version of Microsoft's Media Center, which works okay, but the real gain is the ability to run more than one DVB tuner card without issue.
Vista Premium/Ultimate has a Media Center front end which is much better than XP MCE's and doesn't have the DVB tuner limit. It does require higher end hardware (that is Vista certified, etc)
Software:
MythTV is an Open Source add-on for Linux. Seems to work well, constantly being upgraded, changed, updated, etc. It is Open Source after all.
Media Portal is a Open Source (free) add-on for Windows. Like any Open Source product there are tons of tweaks and changes available at any time. Works fairly well and has the capability to use a central Media Server with all of the tuner cards built into it and then you can install the Media Portal Client on whatever machines you want to connect to the media server to watch TV, view pictures, listen to music, watch movies, recorded shows, etc. The server piece uses a SQL back end and with a central server your hardware is limited to what you put in the server.
There are other Media Center products that can be pruchased, but I don't really have much experience with them as I've only played with Vista Media Center and Media Portal.