Outfitting an generation ship. How many unrelated people would you have to have in order to have a big enough genetic pool for mating to prevent inbreeding?
Practically speaking? A couple dozen unrelated women should be enough. Freeze a few million sperm samples and you're good to go. No inbreeding at all.
If you really really insist on ignoring sperm banks then according to this:
You'd need about 160 completely unrelated, very healthy people.
You'd probably want to screen then beforehand for serious recessive genetic diseases and you'd need to keep careful records of family trees and screen for serious mutations.
Caveat: this is for a limited number of generations(10) and have some additional plans for when you arrive at the destination.