A prefix to verbs, having usually the force of a negative or privative. It often implies also loss, detriment, or destruction, and sometimes it is intensive, meaning utterly, quite thoroughly, as in forbathe. [1913 Webster]

for-, prefix forming verbs and their derivatives meaning:
1 away, off, apart (forget; forgive).
2 prohibition (forbid).
3 abstention or neglect (forgo; forsake).
4 excess or intensity (forlorn).

Etymology:
OE for-, f{aelig}r-