Bleach and steel wool. :evil:
OK, seriously ... I don't know if I personally would call water "best," since there's nothing in it to really cut thru oily fingerprints, smog, or stubborn dirt (and if you scrub too hard, you could rub thru the non-glare coating if the monitor has it). I'm not saying it won't take some surface dirt off, 'cuz I'm sure it will. I just wouldn't call it "best." And cleaners with alcohol or ammonia in them are reputed to strip non-glare coating off (as you pointed out), so I avoid those.
I personally have been using Kensington Screen Guardian cleaner and soft cloths for several years now and the tandem has worked great. Screen Guardian is non-abrasive and, according to the label, suitable for non-glare CRTs, notebook computers, and any screen with a non-glare or polarized coating. That pretty much covers everything, I think. It comes in a small 4 oz spray bottle for $3 or $4. I think I bought my bottle in the bookstore at a local university, but Best Buy or Comp USA carry it too, I think. It's widely available. I usually just put a few sprays on the cloth and rub the cloth over the monitor and it works perfectly. Cheap, simple, safe, effective, and no residue.