If they acknowledge their mistake, acknowledge how it must have hurt you, promise they wont do it again, and demonstrate with behavioral changes they are sincere, it is best to make a sincere attempt to forgive. You can give yourself to remain angry for a while. Then accept their aplology - if not for their sake than for yours.
Corollary - if an apology is insincere be wary of that person. Protect yourself from being sucked into their vortex.