I don't damp mop, our floor isn't supposed to get too wet. Plus it was put together poorly and has big cracks. I use the Orange Glo mopping system. It was about $14 at Wal Mart. It also comes with a refinisher. I have not used that, but another CCer did and said it was a disaster. I think with this product you either love it or hate it.
Writing: a socially acceptable form of schizophrenia.
I used the Orange Glo refinisher to get a nice sheen on the hardwood. I plan on doing this about 2-4 times a year. I also use a Swiffer to clean. I plan on getting the new one that sweeps and dusts, but for right now its just the wet jet.
We just had our wood floors refinished and they said not to use Murphy's Oil Soap on them. Apparently it leaves some kind of residue on the wood floor that is difficult to remove. It gets down into the cracks of the floor and when they go to refinish, it is impossible to remove, even with sanding, and causes all kinds of problems with the new finish curing properly. They told me to use a vinegar and water solution to damp mop the floors occasionally.
We have hardwood floors as well. Our refinisher, like southhavenjen's, told us not to use Murphy's Oil, or even any other kind of cleaner that could leave a reside.
I mostly just dust the floors, but when I do wash them, I use very hot water and vinegar. The hot water will evaporate quickly, so there won't be any water marks or standing water on the hardwood (in case it gets into the cracks and *might warp or damage the boards). It works really well.