I know. Boring. But it always bugs me and this is the only way I'll remember it. (Source)

1. Use "that" with restrictive clauses. A restrictive clause is one that limits -- or restricts --the identity of the subject in some way. When writing a restrictive clause, introduce it with the word "that" and no comma. (However, if the subject is or was a human being, use "who" to introduce the clause.)

Correct Restrictive Use:

The painting that was hanging in the foyer was stolen.

Explanation: The use of "that" in this sentence is correct if the reader intends to single out the one painting that was in the foyer as the stolen painting. However, if there were several paintings hanging in the foyer, this use would be incorrect, since it would mislead the reader into believing that there had been only one painting in the foyer. The restriction here tells us that the one painting that had been hanging in the foyer was stolen -- not the painting in the living room, or the one in the drawing room, or any of those in the parlor.


2. Use "which" with nonrestrictive clauses. A nonrestrictive clause may tell us something interesting or incidental about a subject, but it does not define that subject. When writing a nonrestrictive clause, introduce it with "which" and insert commas around the clause. (However, if the subject is or was a human being, use "who" to introduce the clause and insert commas around the clause.)

Correct Nonrestrictive Use:

The painting, which was hanging in the foyer, was stolen.

Explanation: While this nonrestrictive use tells us that the painting was hanging in the foyer, it does not tell us which of the several paintings in the foyer was the stolen painting. It would be incorrect to use this nonrestrictive clause if there had been only one painting in the foyer, as the sentence leaves open the possibility that there were others.