Is it legal to pass a car on the right when that car is turning? So I've been poring over the bikes SE, and as a recreational biker and an automobile commuter, I'm naturally most interested in topics addressing how bikes interact with automotive traffic.

In one particular question I noticed that it's legal in some jurisdictions for a biker to pass cars on the right at an intersection in order to move ahead of them.

This really surprised me, and it brought up a related question: is it legal to pass a car on the right when that car is making a right turn?? (In other words, a bike passing a car in such a way that if both maintain their intended path, they would collide.)

That may sound like a stupid question, but I have actually seen this twice in the last year. In one instance, I was the driver and I could see the bike approaching from behind at a distance. As I slowed to make my right turn, I glanced back at him and I could see that he was not slowing down. I slammed on the brakes and narrowly missed him as he whizzed by me on the right. I was in the right turn lane, he was originally directly behind me in the same lane, and there is no bike lane on that street.

In an earlier incident, I was walking my dog when I saw a car and bike collide under nearly identical circumstances. The biker was not injured badly but he did wipe out. I found myself sympathizing with the driver more than the biker. The driver was obviously not prepared for somebody to pass her on the right at 15MPH while she was making a right hand turn from the right lane.

Was his bike maneuver legal? Does the driver owe a biker that right of way? And if a driver hits a biker in this scenario, is the driver legally liable?
Is it legal? That depends on the country's traffic laws and on the exact layout of the intersection. The traffic laws that I am familiar with (Denmark, Austria) indicate that the bicyclist you describe was wrong to overtake a right-turning car on the car's right side.

If there is a bike lane that extends through the intersection, then AFAIK the cyclist always has right of way. The car must wait until it can turn without blocking any bikes.

If there is a bike lane that stops before the intersection, or 
if there is no bike lane then the cyclist must place himself in the proper traffic lane. If he wants to go straight, he may not be in the right-turn lane. 

As a driver, what I usually do coming to a stop at an intersection is to place my car so close to the curb that no bikes can pass on that side. Safety benefits:
If they want to go straight, they can safely overtake me on my left side.
If they want to turn right too, they must line up behind me and turn after I have turned.

As a cyclist, I always operate under the assumption that I am invisible, because too many drivers neglect to look for bicycle traffic. (They often neglect to check for any traffic, but that's irrelevant on this site.)

The above presumes right-hand driving.