I've cleaned my monitors with sponges, paper towels, and even shirts with that plasticy design stuff on the front and have yet to scratch one.
I generally agree with the above comments except one should never use Windex. It is ammonia based, and repeated use can degrade/remove the anti-glare coating of the monitor. You are best with plain water or a home-made solution of 50% water and 50% white vinegar. Personally, all I have to deal with is dust, and any soft cloth will do. I like a clean, old T-shirt or a Swiffer sheet. Do not rub hard in any case. Also, avoid any alcohol based cleaner.
You are right about that. I doubt what we used was really windex, I don't remember the ammonia smell, it was a green glass cleaning liquid that we got in gallon bottles and then transferred into spray bottles and used to clean everything (and sprayed our rags, not the monitor). It was probably was something like vinegar and water.