Bill Barnwell of Grantland (who I'm hot & cold with) wrote on this and takes a position I happen to agree with.
Let's start with the obvious one: Michigan–Ohio State. There, a Michigan touchdown brought the Wolverines within one point of their hated brethren, 42-41. With just 32 seconds left on the clock, Michigan head coach Brady Hoke reportedly conducted a quick poll of his seniors and asked them whether he should go for two to win the game. They all obliged, so Hoke sent out his offense, only for a Devin Gardner pass to be intercepted, ending the game.
Was Hoke's decision the correct one? Absolutely, and it's not even close. You're weighing the probability of winning by converting from two yards out versus the probability of winning in one or more overtimes, and the former is clearly greater than the latter. Michigan were 17-point underdogs heading into the game, and if you're a massive favorite, your advantage is more likely to show over a larger sample than it is over a very small one. Bringing the game down to a single play increases the variance of outcomes, which is of huge value to the underdog. Even if the pregame spread overstated the difference in play between the two teams, Michigan would have unquestionably been comfortable underdogs heading into overtime, which would likely take place over 15 plays or more.
When you compare that to the likelihood that Michigan would convert a two-pointer, it's a no-brainer. Their chances of converting from two yards out (if we assume they don't allow Ohio State to score in the subsequent 32 seconds) are far higher than their chances of winning an even game in overtime, especially given the relative strengths of their team. Michigan's defense had basically been run over by the Ohio State rushing attack all day, with Carlos Hyde & Co. combining for 393 yards on 46 carries. Ohio State punted just three times all day. And Michigan's offense had been brilliant, too, with Gardner going 32-of-45 for a staggering 451 yards with four touchdowns and no interceptions (before the two-point play). The Michigan running game had even averaged 4.3 yards per carry, and the Wolverines had scored on each of their three final possessions of the game. Going for two played to Michigan's strengths as a team, eliminated their weakness, and created a higher-variance opportunity for the team to win. It's the right call in that situation every time. You can argue about the play call all you want, but the decision to send the offense out there was correct.
You're playing your biggest game of the year at home as a big underdog to your biggest rival that's on the cusp of playing for a national title while your own team is mired in another lackluster season. A win or loss for you isn't going to have a dramatic impact on your bowl positioning, however, you pull out a win and you're basking in glory while ruining your biggest rival's season.
So why the heck not go for it? Especially from the two yard line? I respect the heck out of Hoke's decision to go for it there. I'd expect the vast majority of college football coaches would cave and kick the extra point and head to overtime. They wouldn't have had the cajones. The ultimate issue I had was with Hoke's playcall there, not going for it.
You could very well not have a better opportunity to win the game then there in that situation. Especially in OT and given the way that Ohio State had been moving the ball, end the game in the 4th. Don't extend the game.