As SyntaxError stated, it depends. If you want a high quality server with good anti-cheating mechanisms, you should validate player positions and prevent them from walking though walls or sending them data that is occluded from their vision. MMOs may take shortcuts because they are already cpu intensive and not many people will care, but games in the 32 player market should support validation.
I actually ignored validation in my last post. Of course some form of preferably low cost validation can also be applied on the server. My main point was that you typically still need client side collision detection at a minimum because otherwise there is nothing to stop a player from appearing to walk through a wall. In fact you will probably fall through the floor pretty readily. The client of course can fix this and put you back where you are supposed to be once it receives an update from the server. However that means you will appear to be bouncing around if you are running against a wall. Or worse you will be bouncing up and down on the ground.
I'm not sure any client/server games use pure server based collision detection. The lag would have to be pretty low and even then I would think the bouncing would be noticeable and very annoying. I was annoyed by a small jittering in corner situations caused by a bug in my CD code before I fixed it. Anything caused by server lag would probably make me want to punch my monitor.
Edit: Actually after reading the OP's post again, I'm wondering if I misunderstood it. I read it to mean all collision detection should be done on the server as opposed to additional collision detection should be done on the server. If he meant the latter .... hopefully I still said something remotely intelligent