Sam Finegold, Harvard Class of 2015 studying Statistics.
This is a difficult question to answer because Harvard's student body is very diverse and quite large, but I will do my best.
Students at Harvard were admitted because they are competitive, and upon arrival at Cambridge, don't suddenly change personalities. That said, there are two major factors that limit competition at Harvard to a healthy level:
Grade Inflation: It is quite easy to get a B or even B+ in most courses at Harvard. This varies by department and by professor, but by and large, Harvard is known for grade inflation. Since many students get high grades, there is less worry about having to best peers in an exam.
It's Harvard: By this, I mean that even if you don't have the strongest GPA in the world, the fact that you went to Harvard will still help you in the long run. You don't have to be top in your class to get a good job (that's not to say you should coast, but it is to say you don't need to get a perfect score on every exam).
Do not get turned off from Harvard because you are worried about the students being too competitive. If anything, I would say students at places like Princeton and MIT, where there is severe deflation in grades, are much more stressful!