A lot of this has been covered above, but here's a good summary. This specifically concerned cleaning and not hygiene which has been beaten to death thoroughly above.
Wipes: These are easy to use and NICE. However, you can run out of them quickly and they can dry up if the pack opens up in your bag without you knowing it.
Water: The wife and I can completely shower with one of those gallon water sprayers (http://www.sears.com/rl-flo-master-1-gal-premium-sprayer/p-07102330000P) from Home Despot. That's half a gallon of water each, and there is usually some left over. Use minimal amounts of water to wet yourself. Soap yourself up. We like Dr. Bronner's (http://www.drbronner.com/) because it's good for everything (incl. dishes and equipment), smells nice, it's good on sensitive skin (which the wife has) and has a label that's weird and fun to read. Then use minimal amounts of water to rinse yourself. It's easier with a second person to help rinse you off. Dr. Bronner's is nice again here because it won't ruin your skin if it doesn't all get rinsed.
SCIENCE!: Rocket Shower (http://10nine8.net/) is a cool product and helps kill all/most of that stinky bacteria without any water. Dry. Spray. Dry. This is probably our Bug Out solution, depending on whether we have water availability or not. The only downside is that the bottle can leak if it's not stored properly.
