As more lamps are put into a series circuit what happens to the overall current in the circuit?

The more lamps you add, the dimmer each would become. The brightness would be the same for each lamp -providing they are all the same wattage. If one of the lamps wasn't working, then none of them would work. If the wattage of the lamps varied, the brightest lamps would be those with the lower wattage rating (yes, this is not a mistake!).

Lamps in series can be dangerous if one isn't working, because the full circuit voltage would appear across the open terminal.