I'm probably an over zealous cleaner. I don't use the bore snake as the single cleaning product solution it was intended to be. I don't think the brush on the snake is sufficient. Also, the first few patches through a dirty bore come out extremely dirty, and I see no reason to put all of that dirt on the snake. I like to start cleaning my bore like normal, without the snake. I wet a brush with solvent and scrub the bore with the brush and a rod. Then I run a patch or two down the bore to get rid of the majority of the crud. Next I run the snake down until the bore is clean. Lastly, I swab the bore with a patch of oil.
I like this method because it takes advantage of the bore snake's large surface area and mega-patch abilities, but doesn't get the snake as dirty, so I don't have to wash it as often.
I also like to take the snake to the range and run it through my bore once before I fire. This ensures that there is nothing stuck in the bore and there are no oil or solvent deposits that could present a safety hazard.
I use a .22 cal snake on my AR-15 and my 10/22, a .30 cal bore snake on my M1A and my Winchester M70 30-06, and a .45 cal pistol bore snake on my Sig/Sauer P220.
I showed a friend of mine the bore snake and now quite a few people in his Marine reserve unit use them on their M16s.