Overtime is a tough subject in sports. In hockey it goes to from sudden death to a shootout. But in football it's even more confusing. NFL football has a sudden death overtime where a team just needs to put a point on the board. While NCAA & Canadian football have a shootout like system where a team gets a chance to score and then the other team gets a chance until one is eliminated. Both systems are flawed.
Here's why: NFL's system means that a team only has to get a half decent run or pass and then they can kick a field goal for the win. That's no fun because it's extremely hard to defend against (given that the team starts with decent field position), it's not because "the other team doesn't get the ball".
The Canadian & NCAA style isn't really fun because it's too complicated. It doesn't give the sense of urgency that you get in sudden death.
My solution: Six Point Sudden Death Overtime. Capitalizes on both systems. Scoring a touchdown is difficult. So reward the first team who gets a touchdown a win. No disrespect to kickers, but a game should not hinge on a single field goal. So the reason for six points is that it requires two field goals to win. Which means that if one team goes for the field goal, the other team would get a chance at the ball, which they could use to score a touchdown and win flat out or tie the game with a field goal of their own.
Now your saying, "But then the other team doesn't get a chance to play if a touchdown is scored" which is right. Like I said, it puts the game in the hands of the defense and offense rather then kickers, but it should reward the team the gets a touchdown. If the team can't hold them to a field goal, they don't really deserve try themselves.
So imagine your at the 30 with a 4th down. Do you throw for the end zone, looking to win the game? Or do you kick a field goal and put it in the hands of your defense? That's why this system works, it equalizes the risk. This creates strategy.
And that's what's important. Football is a game of strategy. And with the NFL's overtime that strategy becomes limited to "Get lucky with a pass/run or get field goal". But this still keeps the excitement.