The overhand flat bend (also known as the Euro Death Knot) is the go to knot for tying two ropes together for rappelling. The primary reason we use this over another knot is because of the way it rides over the terrain when you pull the rope. The knot exists on one side of tied ropes which makes it less likely to get caught when you pull the ropes...
As Julie notes, some people are concerned that the overhand flat bend will roll over on itself and roll off the end of the ropes. In the video, she shows to tie the knot pretty far from the ends of the rope. This length makes it impossible for the knot to roll. There are a couple of other things you can do to keep the knot from rolling as well...
In this first photo, I tied an extra overhand around both strands.
This would decrease the liklihood of rolling.
In this second photo, I tied two overhand flat bends and seated themselves together.
This is my preferred style and I tie my cordelletes into loops with this as well as my ropes.
Some people think that if they tie two ropes together with a flat figure-eight that it will be stronger. Ironically, this is incredibly weak and can roll with as little as 2kN of force (under 500lbs). There have been fatalities from using the flat figure-eight to tie two ropes together.
Julie goes on to talk about tying barrel knots in the end of the rope. She recommends triple barrel knots, but a double is fine, as long as it is pulled tight. A loosly tied double barrel knot can become untied.
A double barrel knot.
Historically climbers and guides didn't tie knots in the ends of their ropes. They were afraid that the ropes would get caught below. That is changing. There have been way too many accidents because there were no knots in the ropes. If you're worried that the ends will get caught below, simple tie an overhand or an eight in the end of the rope and clip it to your harness during the rappel...
--Jason D. Martin