Sorry, I'm a massive pedant, you'll have to excuse me.
It's 'who' when it refers to the object of a noun, like it does in your sentence ("Who is the recipient of this letter?") and 'whom' when it's the subject ("Whom is the letter addressed to?").
Like I said, sorry!
hmmm... I think you have that backwards, no? Normally "pedants" insist
who must be used "nominatively" (i.e., by analogy to Latin, when it is the *subject*), while
whom is the objective (used for objects). Your two examples are right by these rules, however. In the first case,
who is "nominative" because it can be thought of as occupying the "subject complement" spot (i.e. in "The recipient is who"). In the second case,
whom in "objective" because it can be thought of as occupying the object slot of the prepositional phrase headed by "to", i.e. ("The letter is addressed to whom?").
Now, I've got scare quotes around "nominative" and "objective" because they are misleading to say the least. "Nominative" (
I, he, she, who, etc.) forms do not always appear in subject position, and "objective" or "accusative" (
Me, him, her, whom) forms do not always appear in object positions. Since at least Shakespeare, writers have very often used
who and
whom in both places. It is not until the 18th century English grammarians that, again on spurious analogy from Latin, people thought you *needed* to use "whom" in all object slots.
The
facts of actual usage are of course more complicated and apparently seem not to have changed much since Shakespeare's time (in written English; in spoken English,
whom is quite rare and mostly found in self-consciously formal or elite dialects).
Merriam-Webster's Dictionary of English Usage has a great section on the whole thing, with loads of examples. This paragraph sums up some of the facts nicely:
"To repeat, our evidence shows that present-day uses of
who and
whom are in kinds just about the same as they were in Shakespeare's day. What sets us apart from Shakespeare is great self-consciousness: the 18th-century grammarians have intervened and given a reason to watch our
whos and
whoms."