Haha, I'm in the same situation as you described, my GPA's around 3.67 unweighted thanks to a personally rough junior year. Of course, I'm not actually applying to Harvard (or any college remotely close). To be honest, anyone who has below a 3.8 unweighted probably shouldn't be looking at Harvard, since you start to get that "I know I won't get in, but just imagine how awesome it'd be if I did" sort of mentality that ultimately only ends up disappointing. Unless you are a child prodigy at something, come from a super rich family, and/or go to an absolutely ridiculously difficult highs school in which no one has ever gotten a 3.8+, it's just not going to happen. Harvard attracts the best, most gifted minds from all over the world, so the competition isn't even proportional compared to the sorts of stats expected of an applicant.
Now, if you did something extraordinary that has changed the lives of many people, that could certainly be a sort of foot in the door that really gets you noticed, and you could try explaining why your GPA is so low, but short of finding out you have cancer as a freshman or something, I don't think Harvard will honestly even consider your application after a cursory glance. There's just too limited of a number of seats for too great a number of amazingly talented students.
However, I think you can partially overstep that boundary if, by some amazing writing, you could demonstrate that you want to go to Harvard more than anything because of the great academic opportunity and the culture and such, completely regardless of its name and prestige. I mean, as if it were still your number one choice even if it was a no-name school (hahaha) in the middle of the desert with an amazing academic program. Just, keep things in perspective. It's okay to reach for one's dreams on principle, but not everyone successfully attains their dream, sadly.
(P.S. A 2400 would also be mandatory.)