(I have written on this subject before, but because my LJ won't let me browse my archives without booting me out, you'll have to take my word for it.)

That and which--a challenge to writers everywhere. Reading submissions these last two months has really driven the fact home for me. I have only read TWO submissions this entire two month submission period that were not that/which challenged. So, after a long absence from these pages, I give you:
THE BOGWITCHY GUIDE TO THAT AND WHICH

THAT is a restrictive clause, part of a sentence you can't get rid of without changing the meaning, because it RESTRICTS some other part of the sentence. For example:

Mice that don't like cheese will never fit in with mouse society.

It doesn't matter whether or not this statement is true; what does matter is the THAT DON'T LIKE CHEESE cannot be taken out of the sentence without losing all meaning. It's a restrictive clause. Without that clause, the sentence says that no mice will ever fit into mouse society. WITH the clause, it's only those unfavorably disposed to cheese that won't.

WHICH is a non-restrictive clause, part of a sentence that can be left out (not which can be left out!) without changing the meaning. Non-restrictive clauses require a comma, or commas. It's an easy indicator. Restrictive clauses don't usually require commas.

The building, which stood on the corner of 1st and Grandview, was demolished in the Great Mouse Rebellion.

WHICH STOOD ON THE CORNER OF 1ST AND GRANDVIEW is the non-restrictive clause. It is an added bit of information that can be removed without actually changing the meaning of the sentence. And there is your biggest clue--if you can take out the clause without changing the general meaning of the sentence, use which.

The above is an example of a non-restrictive clause plonked down in the middle of a sentence. The ones tagged on to the end get a little trickier.

The building was demolished in the Great Mouse Rebellion, which was not a happy event for anyone.

With the comma + which, the above sentence says that the building was destroyed, and that its destruction was not a happy event for anyone.

Take out the comma in the above example, and now you need THAT:

The building was demolished in the Great Mouse Rebellion that was not a happy event for anyone.

--and the meaning of the sentence changes. It says that the Great Mouse Rebellion was the unhappy event.

See the difference?

The most insidious that/which challenge I have seen so often used lately is a misguided comma followed by an equally misguided WHICH.

They sat on the swing near the fountain, which stood surrounded by tall trees, like a miniature forest in the city center.

Why is WHICH wrong in this sentence? There are commas! But if you take out that clause, the sentence says that the swing near the fountain was like a miniature forest in the city center, not the tall trees. The sentence doesn't make sense. The sentence can indeed be rearranged to make that clause non-restrictive:

They sat on the swing near the fountain, which stood surrounded by tall trees like a miniature forest in the city center.

Or it could be written as a restrictive clause:
They sat on the swing near the fountain that stood surrounded by tall trees like a miniature forest in the city center.

Meh--I don't like either sentence. Each one gives a slightly different meaning, but clear enough and close enough to evoke the same image. Each is grammatically correct, but wordy. And that brings me to my last point--that and which tend to be filler words. I don't like filler words. They're the ones I end up delete-delete-deleting when I edit. They're words we lean on when connecting thought to image, image to thought. Even when used correctly, paragraph after paragraph of that and which bog a story down.

Like adverbs, I prefer to use that and which (especially which--it always sounds awkward to my inner-ear)sparingly. They're necessary. They're beneficial. They can do the job when called for; just be aware of how often you do the calling.