The New Apple TV (generation 2 boxes) and many new TV's with internet connections have access to a number of services. I am not sure if NFL games are there yet, but I have seen NHL and I think NBA "apps" on a recent install of a Samsung TV.
Setanta sports is on line with Soccer and rugby.
I have to imagine the NFL would have something, if not they are missing the boat, lots of money to be made from on line subscriptions.
I use an antenna for all the local HD channels (Toronto and Buffalo) and can watch just about any other programming through on line downloads. I may not be able to watch some programming on the very night it was shown, but typically within a day or two after.
Shows from A&E, Discovery, History etc are all easy to find.

As far as tech savy.. Apple TV is probably the easiest to use and I offer it to my clients (all have Rogers or Bell and just like to have more movies etc available)
Using a computer and setting up something like Boxee is not really that hard, but it does take time and effort to find and download what you want to watch, and keeping things organized can also require some effort.
I picked up an Acer Revo computer (very small form) and also have an external HD for storage. All works well for my uses.
There are a number of sites out there for streaming or downloading TV shows and movies. Some charge monthly fees, others are free to use. A quick Google search will help you find your way into all this and then you can decide if it is something you want to go into further.
Once again, not for everyone and there are likely some frustrations along the way.