It's taught in the UK and you will fail a driving test for repeatedly failing to set the handbrake when you should have. Basically if you are stopped long enough to think "Should I use my hand brake?" then you should.

A few reasons:

1) Your car won't move regardless of what happens with your feet, eg. if you are hit from the rear at a junction you are less likely to be shunted into crossing traffic, or if (say) you get leg cramp and let go of the brake you won't roll and crush a pedestrian who was crossing between cars.

2) You don't dazzle the car behind with your brake lights.

3) Holding the brake pads onto a hot disc can transfer pad material and cause uneven wear. (possibly BS)

edit: I personally use it all the time because as mentioned it also allows you to set the clutch at the same time as releasing the brake, meaning you can move away much quicker.