The screen on my laptop is starting to look pretty bad, between fingerprints, and now, thanks to the dog, doggie drool. I've tried wiping it with a dry cloth, but that doesn't seem to do much to the fingerprints especially. Can I use Windex or some such if the laptop is off?

Don't spray anything on the screen!

Wipe it with a damp cloth. Persistent glop, such as tobacco smoke, can be removed with an industrial alcohol wipe.

I'm guessing that I should do this when it's off. Will a Windex wipe work?

I suggest the dish washer. Top rack is best. Open as wide as it will go and lay screen side down for best results.

I don't have a dishwasher

Sometimes they say not to use Windex. But it's only a few drops, it's only on the screen for a few seconds, and you don't do it very often. So I use Windex. And I got a cloth at the computer store.

Google "clean laptop lcd screen" and a bunch of reasonable approaches come up. Most have to do with using clean cloths with pure water or a dilute isopropyl alcohol solution. Just be gentle while cleaning... drag the cloth in one direction and, if you can't find a clean cloth, DO NOT substitute sandpaper.

I got a package of ten screen-cleaning wipes for a few dollars at a computer store a while back. (I think it was CompUSA, which says how far back it must have been and isn't an option any more.) Each one has two foil packets, much like the ones for most towelettes. One is wet. You wipe the screen with that one first. The other is dry; you use it second to dry the screen.

Works great, hasn't scratched the screen that I can tell.

I also saw a product where you spray cleaner on and wipe it off with a foam eraser for sale at the DTW airport last month, near the Mexican restaurant with the great margaritas. Seemed to work fine when I tried their demo unit on my laptop. Didn't buy it because I still have some of the CompUSA sets left. I seem to recall it was more than just a few dollars, though.

I've been told not to use Windex because of the ammonia in it. I use a spray for laptop screens. I've picked them up in office supply stores and at the Apple store (as overpriced as everything else at the Apple store, but don't take my Mac away!)

A bit off-topic for this thread - but if you want to be cured of this concern, stop in at the London Apple store, as I did yesterday (in town for the traditional Presidents' Day FT Do), and compare prices. They probably bear the same relationship to other UK prices as US Apple store prices bear to other US prices, but they're still scary (to this Yank). The MacBook Air section, by the way, was mobbed. I didn't watch it long enough to see if anyone was buying, but there was sure a lot of interest.

There was a thread recently in which someone from the UK was trying to determine the downside to buying his expensive electronics in the US and bringing them back with him.

I'm told that in Italy, Apples go for the same price number as in the U.S., you just replace the $ with a €.
So, if it costs 1000 dollars in the U.S., it's 1000 Euro in Italy. (a 50% markup).

As to the OP's topic- I've had my Thinkpad x40 for 4 years. Every once in a while if I notice it's dirty I wipe the screen- with the corner of my shirt, the back of my hand, or a kleenex. It's none the worse for it. No significant scratches, the screen is still bright and clear.

Ok, so Windex is out. I guess I'll try an alcohol wipe, or some such, because just a dry cloth isn't cutting it.

This "old" thread might shed some light (on your screen, I suppose... ):

How do you keep your laptop screen clean ??

Water and a microfiber cleaning cloth is all you really need. Use a new cloth dedicated to the computer so that it's not contaminated with other cleaning chemicals. Apple used to include cloths with some LCD screens that had a slightly different texture that works particularly well, but any microfiber cleaning cloth should be okay. (Also good for cleaning eyeglasses.)

What I do is dampen a small part of the cloth with water and wipe the screen. Then I go over it with a dry part of the cloth. This won't do much with a standard cotton cloth or such, but with the microfiber it works well. If it's been a while and the marks are really stubborn (generally oil from your fingers, either from touching it or from the keyboard while it's closed) I might have to repeat the process to get the best results. But it always has given me results. There are pads you can buy to put between the keyboard and screen while the laptop is closed to protect it somewhat. I keep meaning to try one but after a few years now of seeing them I still haven't.

Do not use a paper towel, tissue, etc. Too scratchy, even if it seems otherwise. (A little tiny dab here and there probably won't hurt, but don't take chances when trying to do a good cleaning.)