the passive-agressive act of dramatically apologizing not only for an action which one has committed, but also for things which one has previously committed, has not committed, and would not likely commit, all in an effort to reduce one's culpability for the central action in question. This is similar to a strategy employed by jewish grandmothers, where one apologizes for all things that have ever happened, whether good or bad.
Example of a "Letterman apology":
Dave: ... so my apologies to subjecting them to that vulnerability and being brow-beaten and humiliated, it never occured to me, and as a matter of fact Alan Coulter kept wanting to know if we'd had sex, do you remember that Alan?
Alan: I did and I don't remember.
Dave: So I'll just say I'm terribly sorry ... And now, also because what can it hurt, once again I'd like to apologize to the former governor of Alaska, Sarah Palin...