In the Marines during exercises out in the desert there were times when I didn't have a chance to shower for around 4 days; some times there was spare time for a "field shower" (just rubbing yourself down in key areas with a wet cloth and soap), but other times not even that.
As for by my own choice, two days max. When I wake up the third day's morning (48 hours), I feel so nasty I just HAVE to jump in the shower first thing.
I often wonder how often women do this sort of thing as opposed to men. Of course women are so self-conscious about even being perceived as dirty (never mind actually being dirty, something men can take pride in in some situations), they will probably not admit to having EVER gone a day without a shower even once of their own volition. The reality is of course otherwise.