Any roots circling around a pot are useless. That's the main rule. So there should never be any roots that are longer/taller than the pot, as James suggests. Only reason to cut any more than that is if they clump up when you are putting the tree back into the pot. Imagine this jellyfish shaped thing. It's hard to get it into a pot and keep the roots spread out as they should be. You put the tree in, dump mix in, then you have to kinda pull up on the tree and shake it a bit so that the mix goes below and fills in the spots. But this process is imperfect and often results in either compressed roots or air pockets below, or both. So that's why you might want to cut it back a bit more. In James' photo, most of the roots he has left have enough girth that they are not going to just flop around when you put in the potting mix, they are going to more or less keep their shape. If he left on those long stringy things, they would end up compressed together, which is not what you want.
An alternative to a full root prune is a partial one, where you may leave some of the mix on the interior part of the rootball, but you'll cut off the outer edge all around and at the bottom, and pull out and get rid of anything that is winding in/out and around. This may be faster/easier and may shock the plant less. But probably a full root prune is required at some point. Just not necessarily every time.
I am hoping that by using fabric pots I will end up doing less root pruning. Time will tell how much root circling still happens. Even if circling is completely prevented, there is still the issue of compression, but that can be alleviated by just cutting some chunks out of the thing with a sawzall or hole saw and/or putting in a bigger pot.