One of the concepts described in "Drive" by Daniel Pink is that of a FedEx Day, where employees can work on anything they want for a 24-hour period. There are just two caveats: the tasks they perform can't fall under their regular job responsibilities, and they must present what they've made to their colleagues the following day.
The FedEx Day was coined by Atlassian, an Australian software company; the company still runs FedEx Days once per quarter. The initiative is so named because employees must deliver something overnight -- just like FedEx. Atlassian completely supports FedEx Days, so much so that all meetings are canceled or rescheduled if they fall on a FedEx Day.
PAT Learning Solutions organized a FedEx Day last year and got "very positive" feedback from participants. Many developers worked late, and three voluntarily slept in the office overnight to finish their projects. This video interview between Rob van Lanen of PAT and Rini van Solingen shares more about the company's FedEx Day:
Does your organization have a FedEx Day?