Being a sports fan and a game designer, I can't help but want to modify the rules of the sports I follow. If I were made lord and master of the NFL, these are the changes I would make to improve the game (in order of importance).
Fix Overtime
Overtime in the NFL is broken because it feels very random and often just ends in a short field goal. The college solution is a nice try, but there is a much easier and better way to do this. First, change the end-of-game rules to say the game is over when time has expired and the team with the lead has the ball. This means that a team that is tied or trailing does not have to worry about the clock at the end of the game (assuming they have the ball and are within a single score) and can run a relatively normal offense (and this also makes prevent defenses useless).
After any final possession by a trailing team is done, the game only continues if it is tied (and is now sudden-death, as usual). To eliminate the randomness and the too-common field goal ending, all kicking is prohibited if the score is tied and time has expired (even if it happens in the middle of a drive). This means no punting, field goals, or extra points (kickoffs are not needed either, of course), which means lots of dramatic fourth-down plays. You cannot convince me that this would not be glorious.
Eliminate the Extra Point
The extra point is the most pointless play in football and has long outlived its usefulness. But two-point conversions are cool and dramatic. The solution is to combine the two. Require only conversion tries after a touchdown (no kicks), but only count them as a single point. But then allow the offensive team to keeping trying the conversions until they fail. This means a touchdown would usually be worth 6, 7, or 8 points, but occasionally could be worth 9, 10, or more. While a long string of conversions is really, really unlikely, it does mean that technically no lead is safe (and eventually someone will win a game with a dramatic string of eight or more conversions).
Restructure the League
The most dramatic change I would make is to completely restructure the league itself. I would split it into a premier league of 16 teams and two regional leagues (also of 16 teams each), one in the west and one in the east. This change would occur four years in the future, as expansion teams are created and the 16 premier teams are selected from the current league. All teams appearing in the conference championship games for the next four years are automatically in. If there are still more slots to fill, they are filled by teams that won their divisions but never made it to the conference championship (ties are broken by number of divisional championships, then by overall record for the four years, then head-to-head record, etc.). In the unlikely event that there are still slots to fill after that, they are filled in order of overall record for the four years.
Each league would have four divisions, with each team playing their own division twice and everyone else once (except for two teams each year). The first round of the playoffs would be the second-place team in each division against the division leader to determine who the actual division winner is. The regional division winners then play, followed by the premier division winners a week later. The next two weeks are the regional championship games and then the premier league championship (played at the home field of the team with the best record--not a neutral site). Then, a week after the premier league championship (instead of the pro bowl--but this is where all the pro bowl awards and such are handed out), the east regional champion and the west regional champion play and the winner is promoted to the premier league the following year (replacing the team with the worst record, which is relegated to regional play).
These changes would concentrate more talent onto fewer teams, while also allowing a "minor league" for developing players (who could actually play instead of rot on the bench). It would bring the NFL to more cities without diluting the premier league (and with every regional team fan knowing that one day their team could make it to the premier league).