Getting your rope jammed in the middle of a canyon can be a big danger. At best it can be time-consuming and frustrating. At worst it can be expensive, or even life-threatening.
Sometimes you will not even be able to get the rope moving at all when you pull it from below. This is usually the result of too much friction at the top of the abseil. Generally the rope will at least be running through a sling and over a section of rock, but sometimes it will be over several sections of rock, or even around a tree. There are a few tricks that you can use to reduce the friction and make sure it will start to move.
Note that many of these tips rely on the last abseiler either rigging something, or adjusting their abseil. For this and many other reasons, the last abseiler should always be experienced, and in the case of a less experienced party, the last abseiler should be the most experienced.
Pull down test
On any abseil where there is a chance of the rope not pulling freely, you should carry out a pull-down test before the last abseiler descends. One of the abseilers below pulls one end of the rope, and the party checks that it easily pulls through the sling or other anchor. If it doesn't move, or is extremely difficult to move, then the last abseiler may need to consider some of the options below.
Untwist the rope
Trying to pull a twisted rope is harder than an untwisted one due to increased friction. The rope wrapping around itself causes some increased resistance. One strand of the rope can also lie on top of the other one. If you pull the top strand, the force will push down on the bottom strand and make it difficult to move. Untwisting the rope will reduce this introduced friction. The rope can easily be untwisted by someone abseiling down with a crab (on a sling to the harness) clipped to one strand of the rope.
Lay it carefully on abseil
Sometimes the abseil rope will most naturally run over a sharp edge or in a crack, which will increase the friction on the pull-down. This can make the pull-down difficult or impossible. The last abseiler may be able to choose where to lay the rope as they abseil. How well they can do this depends on their skill (and sometimes strength) as well as the nature of the abseil itself.
Rerig the abseil
Just because the slings for an abseil have been rigged in a certain way doesn't mean that you have to use them as is. If the current anchors are causing problems with pull down then you should rerig the abseil if possible. You can use slings around a different anchor, lengthen the slings on the existing anchor, or even use two anchors to change the direction of the abseil. If none of that works, then you can even put a crab or rapide on the sling to reduce the friction. Obviously the crab or rapide gets left behind, but is a few dollars worth a rescue?
By using logs, rocks and similar things, an abseil can be altered to make the pull-down easier. Putting a log under the end of a long sling can lift the sling off the ground and allow the rope to run more freely. If the rope is going to pull through a crack, you may be able to jam a small chockstone in the crack that will prevent the rope from getting stuck in there.
Use an appropriate knot
If you are doing a double rope abseil, you will need to join your ropes together with a knot. Some knots have a propensity to catch on edges and jam in cracks when you pull the ropes down, whereas others tend to slide well. If you are pulling your rope over a sharp edge, you should consider whether the knot you use will slide over the edge or whether it will catch. Common knots used to join ropes together are the one-sided overhand, the rethreaded figure-of-eight bend, and the double fishermans. In general the one-sided overhand is best at passing over edges, but is the weakest of the three knots. Likewise, the double fishermans is the strongest knot, but also most likely to jam in a crack or catch on an edge. You should weigh up the pros and cons and choose an appropriate knot.
Pull the right end
There are a couple of times when you need to make sure you pull the right end.
The obvious one is when you are abseiling on two ropes joined by a knot.
The other is when the rope is running down through an anchor which is lying on the ground. If you pull the top strand of rope, it will push down on both the anchor and the bottom strand and significantly increase the friction. Always pull the bottom strand of the rope in a situation like this.
When I'm worried about which end to pull, I make sure the last person comes down with a crab on a sling around one of the strands of rope to untwist it on the way down. It serves two useful purposes - it gets rid of the twists and lets you know which end to pull.