My mom bought the Bissell steam mop:
http://www.amazon.com/Bissell-1867-7...0738273&sr=8-1
Neither she nor I have tile floors, but it does a good job of getting all the yuck out of the textured vinyl floor in my kitchen (

I want to replace it very soon!). It doesn't use any chemicals, just tap water (or distilled if your water is too hard).
She also looked at the Shark steam mop (
http://www.amazon.com/Euro-Pro-Shark...0738491&sr=1-1), but when she asked my opinion, I told her I'd tried a few other Shark products in the past (a cordless vac and an upright vac), and I hadn't liked them. So she went with the Bissell.