Build a Home Theater PC with an ATSC TV Tuner card installed. What over-the-air broadcast channels you may or may not receive will depend on where you live and the distance from the broadcast towers of each local station. You can use a web site
AntennaWeb.Org to find out what channels *should* be available to you.
Everything else you will need to find an alternative (free/online) source. Some cable channels will place their programming online shortly after it airs on regular cable. For others, you may need to look at pay services like HuluPlus, Amazon Instant Video, and Netflix. Whatever your end solution is, it's going to depend on what you're willing to give up and what you can't live without... programming-wise.
As far as the...