Yes, they do. I use bar soap (usually a "garden" soap meant for heavily soiled hands) and cold water. They get clean (as in white). Cold water is a must, hot or warm water doesn't seem to work as well.
They do wear out with repeated use of course and YMMV, but using these has really cut down on paper towel usage for me.
I use them in the kitchen mostly, generally to clean counter tops, dishes that need hand washing, stove tops, and my floors when I spill something, so they get pretty dirty and gunked up with a wide variety of things. They also do furniture clean up well. They hold up well to standard cleaning products (from 409 to Comet). I doubt motor oil or similar would clean up well, but I have shop towels for that sort of mess.
When I bought my roll it was $6, I see they've now gone up to $7, but I feel like it was well worth it for me.
As an aside, my wife was very skeptical about them when I got them, but now they have her seal of approval
