Hoppe's Bore Snake may be the best weapon cleaning tool ever invented. When we deployed to Iraq in 2004, a high-speed sergeant in my platoon had one of these and it got passed around all year. Just drop the weighted end of the rope down through the chamber, and pull it through the bore. The brushes are built in, and the soft part of the snake acts as cleaning patches to make the inside of your barrel sparkle. You can use any kind of solvent on it, or just run it dry, and when it gets dirty, stick it in your cargo pocket (to keep it from wrapping around the agitator) and machine wash. They come in every caliber imaginable, including .50 cal and all shotgun gauges. 5.56mm is .22 cal, 7.62 is .308.
I asked my wife to send me one when I was deployed, but she got the wrong thing (thanks anyway, honey) so I actually tried to make one out of 550 cord and some thicker nylon cord. It kind of worked, but when I went home on leave I made sure to get the real thing. Together with some spray Teflon lube (Remington makes some called "Rem dri-lube"), we all had clean bores and well-lubricated bolts.