If I have one object hidden behind another, clicking the visible one multiple times in Object mode alternates the selection between the two. Is it possible to turn this behaviour off, and make the selection stick to the visible object regardless of how many times I click it, similar to Limit selection to visible in Edit mode?
You're talking about this button in edit mode? No, I don't think there's an object mode equivalent. I don't see how it would be very useful, however, what's the problem?