There is no way "legal" way to watch live streaming NFL games online without going through a cable provider. NFL does not allow any websites, even their own, to stream live NFL games. This is due to the huge contracts that the NFL has with CBS, FOX, NBC, and ESPN. If the NFL were to stream live games online, it would take away viewers from these stations, resulting in a loss of advertisement revenue.
If you want to watch full game replays online, after they have happened, NFL offers NFL Game Rewind. This requires a paid online subscription.
If you have you heart desired to stream a live NFL game on your computer, you can buy a special package with most of your cable providers that allows you to watch live TV on your computer. This doesn't effect the contracts that NFL has with certain channels because it is the exact picture you would be seeing if you were watching on a TV. Thus giving CBS, FOX, NBC, and ESPN their view rankings and ad revenue.
To sum up...
- There is no way to watch live NFL games online unless you buy a package from your cable provider.
- There is no free service which allows you to watch full game replays other then NFL Game Rewind.