Marches are considered to be n 2/4 time, not 4/4. The time signature that you are listening to, or at least, we suppose you are listening to(since there are several tunes you could be talking about) , is not 3/4, it is 6/8, which is a compound time built on 2/4 (think of it as 2/4 with triplets on each beat, which, in essence, is what it is).

Most. or at least many military marches from before the Sousa era tended to be in 6/8, and in fact, Sousa tended(at least, I was told by a friend of my father's, who had played with Sousa) to play in 6/8.

The triplets give a lift to the marching beat, and when you travel on foot, after the first four or five hours of marching, you need all the lift you can get. The fife and the multiplicity of different types of pipes, lend themselves to playing triplets well, and when you think about it, many of our tradtional melodies, especially for dancing, tend to feature a triplet feel, from jigs to reels, to strathspeys, to hornpipes.

As time has past, and the uses that these melodies have been put to has changed, the melodies have gotten to be played with different pulses and different tempos

Since nobody has posted them yet, here are my two favorite MIDI's, Lesley Nelson's arrangement of When the King Enjoys His Own Again and John Renfro Davis' military sounding 6/8 version of The World Turned Upside Down