Commonly, for peak fitness, the two most progressive feilds tend to be that of performance athletes and the armed forces. Some of the armed forces becomming considerably effective with their techniques. Clearly these levels of effort expenditure are not for the taste of all, but it's possible to take similar techniques, and simply do them less.
Not only around the desk, running on the spot rapidly is equally effective. Star jumps/jumping jacks are also great cardiovasicular - 150 of them sets most people panting.
Various forms of press-ups, pull-ups, "planking" or otherwise using the body itself as a form of resistence in order to focus effort into specific muscle groups should provide a level of resistence you can "safely" cope with, leading to overall tone and with increased effort scale itself proportunately over time. A few such trivial excersizes repeated in small number, say 25 press-ups, 150 star jumps and 45s of planking - cost less than three mins - to some vague regularity(rest is as important, if not more so, than effort, but whilst one muscle group is resting one day, you can work on another) and through regularity, and scalar increase over time until the point you feel satisfied, it's possible to maintain a reasonable overall level of fitness with minimal specific effort.