I believe that flight crew naps are allowed for transocean flights now by many airlines. I think it's an airline policy, not by government regs.
At McKinney, Texas, the tower controller is on-duty in 30 minute shifts. There are 2 guys in the tower most of the time, especially during daylight hours, but sometimes only one controller on off times. When 2 are present, you can set your watch by when the voice changes over the radio.
Usually, the one controller runs both tower and ground control, unless they get really busy. It's rather rare that that happens -- maybe once or twice on the weekends when all the Sunday flyers come out. On those occasions, the guy on break from the tower position runs the ground control positon.
McKinney Tower is not a high stress controller position, however.
I've had tours of both the Fort Worth ARTCC and DFW Tracon through a program that the FAA calls Operation Raincheck. There, the controllers work in pairs -- one controller working the radar and aircraft communications, and the second working the traffic strips and coordination with other sectors. I don't know the timing of the controller breaks there.
cubflier, I don't really know enough about how they run the operation to have an opinion. If the breaks are 20 minutes or so in duration, that's hardly enough time for a nap to be of use. On the other hand, if they an hour break after 4 hours on a radar, then a nap might be beneficial to controller alertness. I don't know enough about it.
I see that the NATCA (controller union) is complaining that their new contract will result in more fatigued controllers.
http://www.foxnews.com/story/0,2933,211803,00.html
Hank