i'm a member of the ripit club.
i very often tear my fabric in half lengthwise. it helps me see the straight of grain and it's easier to fold for cross-cuts without elbows. it also gives me a good idea of how the fabric will behave and hold up over time.
like others have mentioned they do, i also tear across when i want a quick hunk off the end of a long stretch of fabric.
i'll tear a rough-estimate lengthwise for borders and then trim to size.
because it does often result in fringey ruffles at the end that have to be trimmed back, if i'm not sure i can afford to waste even a half-inch, i take the time to measure and cut.
i also find that trying to tear a fabric is a more reliable test of whether or not it contains polyester. as others have pointed out, poly is either difficult to tear or won't tear at all. i can't always tell the difference from a burn test.