I cut the cord about 3 months ago. I have an outdoor antenna that gets me all the locals in HD – and yes the HD over the air is not compressed, so its a better picture. I live at the top of a downtown building, so you definitely need to check your reception.
I use a media center PC (with 2 TV tuners) for my main TV, so I can record and watch at the same time. I also can surf the web and stream anything I can find interesting (Amazon VOD, all the cable networks have free content on their websites). I upgraded my Cox internet to Premier ($60/month). The cool thing about still getting internet from Cox is that you can get any of the content from ESPN3 for free because you are still a subscriber. I also have a Hulu+ subscription ($8/month) so I can get most all of the cable shows that I want (Daily Show – Comedy central).
For my 2nd TV I have a Tivo which also has 2 tuners and is web enabled to get Netflix, Amazon, Youtube, and Hulu+ soon. So if you don’t want to go with a full PC a Tivo is not a bad option.
The only thing I miss is Indycar & F1 racing (they do not live stream their races), but you can always find an illegal stream on the net.
One other note: if you still get you internet from a cable provider they still have to deliver the local channels over your cable, so for Cox channels 705 – 711 are all the locals in HD, so technically you don’t need an antenna.