Introduction: Repair a Torn Belt Loop
I tend to wear a good pair of jeans to death, and a common failure point is that a belt loop comes off. Generally this is not due to the stitching coming out, as many tears are. On belt loops, what usually happens is that the fabric of the pants fails at the point where the loop is attached, and rips a hole. This is, however, mendable with very little effort, in ten minutes or so.
Step 1: Reinforce the Pants
Get a small piece of sturdy woven fabric and cut a backing piece. This should be about an inch or an inch & a half on each side, and cut diagonally, so that the edges will not ravel.
Pin this to the back of your pants, over the area where the hole is.
Using thread that matches the pants (or highly contrasting thread if you prefer), stitch around the hole, avoiding the pins, then back and forth across the torn area. Use the sewing machine's reverse function, angling the line slightly each pass, so that each line of stitching is a millimeter or two apart. When you've done one direction, turn the pants 90 degrees and do a second pass. You should end up with some stitching that looks like cross-hatching, and the hole will hardly be visible any more. The last pictures show this but they are sadly blurry (my apologies).
Step 2: Stitch the Loop Back On
If you haven't already, pick out as much of the old stitching from the belt loop as possible, it may get in the way as you reattach the loop.
Stitch back and forth across the end of the loop a couple times. Then decrease the stitch length and increase the width until you have a thin, short, zig-zag stitch, and go back & forth a couple more times. Finish the stitching in the middle of the loop as the stitching is less likely to pull out there.
And that is it. The mend will likely outlast the remaining loops but of course you can re-do it as many times as you need.