I would forgive the friend and let it go, for my sake rather than the friend's sake.
However, forgiveness would have nothing to do with whether or not I chose to continue in the friendship.
At the very least, trust would be lost. If I chose to continue with the friendship, I would show great caution until that friend showed that trust was warranted again.
Assuming that this was a close friend - whether or not I had anything more to do with my friend, or what future relationship I chose to have with my friend would depend on the circumstances around the theft and the history of the friendship. For example, if a friend was a lifelong dear friend who was temporarily desperate for money, and stole money from me, I'd let it pass, but expect the money to be repaid as soon as the friend was financially able to. However, if the same friend stole enough money that the friend knew it would cause me harm, or stole something that he or she knew had great sentimental value to me, I'd feel that the friend was less devoted to the friendship than I had thought, and I'd put some distance between me and that person.
If the friend stole from me to supply a drug habit or for some other reason that my friend would know I would not condone in any way, I would tell that friend to leave me alone until the reason for the theft was no longer a part of my friend's life.
If the friend stole something from me purely because he or she wanted it, I'd also let the friendship go, because it would not be a real friendship if that happened.
If this was a casual friendship, the friend's circumstances would have to be truly desperate and the friend would have to know that what was stolen from me would not cause me damage before I would even consider having anything to do with that friend again.