Generally you get a fountain drink (soda, lemonade, etc.) Some places will give bottled water. I imagine a regular coffee would be allowed. I highly doubt you could get a speciality beverage or milkshake at a CS.
I think that we always ordered large drinks but not sure. We always ask for no ice in the sodas and then I ask for a couple of cups with ice. You would be surprised how much more soda that you get. Not one of us leaves thirsty.