How many people are required to maintain genetic diversity?
Actually it is a very important question for laboratory animals (and, I imagine, endangered species) and was calculated to be 25 couples.

With any number of animals (including humans), there is always some inbreeding happening, but you can reduce it with the number of breeding pairs and careful pairing. When you get to 25 pairs (50 animals) and have complete control over pairing, you can sustain the genetic diversity practically infinitely (especially if you take into account spontaneous mutations).

Of course, such control over who can have children with who (plus whether one is at all allowed to procreate and what will be the sex of their children!) would be questionable morally, so in case of populating a distant planet, we would need a larger group, to provide for sexual preferences, fertility problems etc.

Some information on laboratory outbred stocks.