My boss, Steve (why are there so many Steves?), recently inspired me to re-read David Allen's Getting Things Done. Allen has a point that applies perfectly to me: I don't get stressed out about having to do things, I get stressed out about having to remember things. His solution is equally obvious - write stuff down. Whenever you think of something that needs doing, either do it now or write it down. Review your big list of stuff weekly.
This all works very well for an individual. For an organization to be effective, it should follow the same principles. Write everything down in a place where everyone can see it. At work, we use an in-house ticketing system that parallels many, many similar systems in IT departments across the world. Basically everyone has a TO DO list. You can add stuff to someone's list, finish stuff on your list, or move stuff from your list to someone else's. When a task is done, it goes back to the person who created it to check.
It's simple, and it works amazingly well. A manager can very quickly determine if an employee is overloaded with work and sort things out accordingly. We have a simple 1-6 numeric priority system that tells everyone the difference between background tasks, regular tasks and "do this right f*cking now" tasks. More importantly, we don't lose stuff. If we decide not to do something, someone has to put their name on it and say so. We only lose stuff that isn't in the system.