Me too, but when I do Word suggests I add the comma. I never know whether to the 'that' or 'which', and when the comma is entirely appropriate. I often resort to common sense, but often I give up and let Word confuse me even more.
I really wish I had superb grammar.
I'm sure if you simply google which/that, it'll tell you which (lawlz) to use when. But to my understanding of grammar, what Word's recommending is arse-backwards.
Anyway, I'm gone!