If you're just happy with OTA transmission, it can be done no problem.
My boss actually does this. He has a Win7 box (and Thermaltake case that supports Media Center w/ remote) and simply put in a Hauppauge tuner.
He's integrated it with Media Center and records, plays back, watches, etc whenever he likes.
It's actually his main TV and watches/uses it nightly.
All recorded or watched live in the HD 1080i transmission of OTA. He has a few TB drives to handle all the recording, which...can handle a huge amount.
Media Center records perfectly (although once and a while he does have a time issue being off since there isn't a cable company/cable box synchronizing the transmission). Recording features from one time deal to recording the whole series.
He's extremely happy with it and doesn't even touch cable/satellite/etc...
The only problem I find is...there are no sports channels. Something he doesn't care about however.
He's actually picking up 20 channels right now with a directional antenna (much better than OMNI) and lookin' to put in another directional to pick up about 15 more stations the other way.
You can get away with just using a dual core system and 2gig RAM (I'd suggest 4gig though).