Sometimes flight attendants force passengers to put their carry-on luggage in the baggage hold, in case there is no more space in the cabin. In that situation, is the passenger entitled to some compensation?
There is no right (for you as a passenger) to have carry-on luggage; and as safety of the aircraft is paramount, having no place to stow luggage in the cabin is a risk - as it can turn any item into a projectile if there were turbulence.
So the airline is well within their right to stow the luggage in the cargo hold.
Further, many times if this is the case - the luggage is provided to you at the jet-bridge/staircase on arrival.
If you have some medication or other such items in your carry on and you are asked to stow it in the cargo hold; you should remove these items (for obvious reason).
Now, if the airline has a specific fee for carry-on luggage (that is you have to pay for this privilege) then you might be liable for some compensation.
Although, I don't know of any airline that does, but you can never assume things - especially with LCC (low cost carriers).