I use one of those Vileda mops and the Mr Sheen liquid cleaner for wood and laminate floors diluted appropriately in water. If you get the Vileda mop-bucket you can wring out the mop until it is just damp. I find the combination does a great job.
As I suffer from asthma, when I change the bed-linen I wipe down all the surfaces with a solution of cold tea and water after vacuuming. Then I wash the floors with the same solution. It helps kill off house dust-mites and neutralises their droppings.
The floors in the house are a combination of wood and tile with only one hearth-rug downstairs - made from bamboo!