Pressurized, yes you should stop, put it on a timer with your lights.
diy - no real need as it is not that efficient
other (hagen co2 type) - not necessary as it is not that efficient
You risk possibly gassing your fish with the excess concentration of CO2. At night (or when your lights are off), your plants will not be using CO2, rather they will be letting out CO2 themselves, as they grow. You are also risking draining your CO2 tank faster than needed. Even though a tank of CO2 is relatively cheap, filling it up more often than necessary can put a dent in your aquaria budget.
As Coach said, a good practice is keeping your CO2 solenoid on the same timer as your lights.
Of course, this is all assuming you're talking pressurized, and not DIY.
I've only used DIY, so I'm not sure, but CO2 lowers pH and you may want to check it during the day and during the night to make sure it's not varying too much. No one else seems concerned about it though, so I'm probably over-reacting, but thought I'd mention it just in case.