The rider going downhill should yield to the rider climbing. That being said, if I'm climbing a sweet dh section and I hear a rider coming, I will often let the other rider go if possible.
The rider coming downhill should stop just b/c its a lot harder to climb than descend so its easier for them to stop and start. It really depends on the trail too but i think most riders either up or down will have some respect and slow down or stop.
I was leading a group ride last night. We had 10 riders and twice had riders that were climbing yield to us. The trail was very narrow and because of the size of the group, the climbing riders chose to yield. We slowed down and waited until they moved off the trail. Most experienced mtn bikers can assess situations like this and make judgments depending on the individual situation. I never assume that a climber is going to yield to me, even in a group ride, but they often do and of course when this happens, we always thank the climbing riders for letting us go.
