OK, I'll play. Including the non-playoff seasons, in chronological order:
2002: It was obvious by mid-season that the team had too many problems (e.g. Steve Martin running his mouth while playing like crap) to be Super Bowl caliber, and at that point we had no real reason to expect them to be a contender every year. On the pus side, this season was pretty strong evidence that that Brady guy was not just a one-season wonder. Suckage factor: 1/10
2005: It's weird - if they had played that Denver game 10 times, the Patriots would probably have won at least six of them. But the actual game was such a multifaceted train wreck that it doesn't really feel like a missed opportunity. The only thing that still bothers me about that game is that Ben Watson was not given justice on the Champ Bailey play. Suckage factor: 3/10
2006: Just awful in so many ways, most of which have been hashed out thoroughly already. I will just add that this was an early example of what would prove to be a recurring weakness at times over the next few years: the complete inability to run the ball effectively when trying to protect a lead. Once Corey Dillon essentially retired mid-game, virtually every single running play (with the exception of some Kevin Faulk draws) went for negative yards - and this against what had been a notoriously porous run defense for most of the season (yes, they had improved with the return of Bob Sanders, but still). Even a D- running game in the second half might have been good enough, but they were a solid F. Suckage factor: 9/10
2007: Next. Suckage factor: 10/10
2008: This one is interesting. Most people will say that they had no real shot at a title run with Matt Cassel at QB, so who cares. Objectively, they may be correct...but man, that team was starting to hum in December, even if against mostly inferior opposition. Lamont Jordan was an underrated pickup that season, and while they were clearly on their last legs, it would have been very interesting to see what the defensive core from the (first) championship years could have done with one last shot at the postseason. Suckage factor: 5/10
2009: I think we all knew for most of the season that this team was not destined for greatness, and Welker going down in Week 17 was obviously a killer. I still expected them to beat the Ravens, but once they fell into the big early hole, I realized that it should have been obvious all along that this was coming. The bright spot from this game was an early glimpse of the ferocious playoff beast that Edelman would become: late in the game, with the outcome already beyond doubt, he fought through what looked like a routine tackle in order to pick up a first down. Suckage factor: 2/10
2010: While 2006 probably hurts more, this game is the one other than the Scottish Game that I find it hardest to even think about, let alone rewatch. As such, I have nothing to say about it. Call it the Irish Game - it can be mentioned, but only when three sheets to the wind. Suckage factor: 9/10
2011: This one doesn't bother me nearly as many posters here. The defense was awful that year, and when it was clear that Gronk was hobbled, the offense was just a borderline gimmicky outfit involving Welker, Hernandez and whatever was left of Deion Branch. They had no business even being competitive in that game, and while of course it was tantalizing that they came so close, it would not have avenged 2007 even if they had managed to pull it off. Suckage factor: 4/10
2012: Looking back on it, I'm surprised that this one did not hurt more at the time. Strange as it sounds now, I think we had grown somewhat accustomed to playoff futility at that point. But objectively, this one was pretty bad - an awful drop by Welker (much worse than the previous SB) and a couple of stupid punts in Ravens' territory led to a bunch of missed opportunities in the first half. Then Talib went down, and we were treated to the Marquise Cole Headless Chicken experience, and then Bernard Karmell Pollard did his thing to Ridley....ugh. To add insult to injury, this game was a chance to end Ray Lewis's career. Silver lining: the Ravens' improbable Super Bowl run led to them giving Flacco that ridiculous contract, so there's that. Suckage factor: 8/10
2013: This team just did not have the weapons to compete with Denver on the road. It was an amazing competitive effort that they ended up a missed two-point conversion away from making it a one-score game at the end, especially with Talib knocked out once again. From my point of view, the worst thing about this game was that having been de facto president of the Alfonzo Dennard fan club, the manner in which he was beaten up and down the field by Demaryius Thomas pretty much confirmed that he was a marginal starting CB at best. Suckage factor: 4/10
2015: As others have mentioned, it was not the game itself as much as the circumstances that caused it to be played on the road in the first place (the Chris Harper punt, Osweiler temporarily playing like a competent NFL QB at just the wrong time, the weird OT decision against the Jets) that are annoying here. But the self-inflicted wounds continued during the game, and were not limited to Stork's head-bobbing. Someone earlier mentioned Collins freelancing on the TD pass to Daniels, but the whole defensive scheme on that opening drive was bizarrely passive, playing right into the few remaining strengths that Noodle-arm Manning had left. Still, given the success that happened on either side of this season, I find it easy enough to remember this game for those two beastly fourth-down conversions to Gronk at the end, rather than the fact that it ended badly overall. Suckage factor: 6/10
2017: This game left a really weird aftertaste due to the whole Malcolm Butler fiasco, and the fact that the defense was simply garbage from beginning to end. Even in the wilderness years of 2009 through pre-Talib 2012, BB had almost always found a way to MacGyver the defense into some kind of passable shape by the end of the season. Even as it was happening, it somehow didn't feel possible that they could just simply...suck. Suckage factor: 7/10