I'm a big fan of the word 'that', but mostly as a replacement for the over-used 'which'. To inexperienced writers, 'which' seems somehow more educated than 'that', so they write such phrases as:
"There will be a newsletter which summarises all our activity on a monthly bases." (Guardian Professional Network, 26 September 2011)
Ignore the obvious howler ("bases"). Clearly the writer wants the phrase "which summarises all our activity" to define the newsletter, thus distinguishing it from all other newsletters. If so, she should have used 'that', because 'that' defines and 'which' describes.
Put another way, a clause introduced by 'which' simply provides more information and could be made into a separate sentence. A clause introduced by 'that' provides essential, defining information. So, the film about Franz von Werra, the only German prisoner of war to escape from the British in World War II, was called 'The One That Got Away'.
In these cases, 'which' should always be preceded by a comma. If it isn't, you run the risk of creating an ambiguity. Here's Jonathan Jones writing about museums:
Does he mean 'that' or 'which'? If, as I suspect, he means the latter, then he should have used a comma. That means the sentence could have been rewritten as:
"In fact, the new Renaissance galleries at the V&A do include activity areas. Visitors of all ages seem to enjoy them."
If he meant 'that', then he is distinguishing these activity areas from other activity areas – presumably ones that visitors don't enjoy.
But 'that' has other, less noble uses. It's often a sign of wordiness (and the grammar checker in Microsoft Word is good at spotting this). Sentences containing "it is … that" are almost always wordy and over-written, as in this example from a recent report I read:
"It is quite likely that we will see further casualties"
That could have been written much better as:
"We are quite likely to see further casualties"
We have replaced 'it is' with 'we are' and 'that we will' with 'to', saving two words (20%). I'd get rid of 'quite' as well (and I nearly always do), but let's not cloud the issue. If I were boiling it down to its essentials, I would have simply written "further casualties are likely", reducing a ten-word sentence to four words, without any loss of meaning.
Moral: 'that' defines, 'which' describes