I am using a Palm T|X PDA with a thin plastic sheet on the screen. It isn't an anti-glare, it is meant to protect the screen only, but I guess the anti-glare ones are similar.
The touchscreen is still usable. It is a bit less responsive, but not by much. I can use it with both finger and stylus.
It is also a bit uglier, because it is very hard to paste the thing perfectly. It is a bit like pasting wallpaper, but it is transparent - you not only have to worry about trapping air bubbles, but also every dust particle beneath the filter stays there forever, quite visible. And if you happen to touch the underside once, be it with a finger or something else (I used tweezers for pasting), you leave a mark there.
Depending on the surface, the filter could have a bit more traction than the glass surface of a touchscreen, making sweeping gestures a bit slower than usual (but still it isn't a big problem for me).
It is certainly removable. I don't know what kind of glue the filter's manufacturer uses, but it will probably come off without the need for cleaning except for some water and a microfibre cloth (the kind sold for cleaning glasses). This is how I clean the screen when I change my screen protector. If in doubt, get filters made by some well known brand manufacturer, I use screen protectors from 3M (don't know if they are selling filters).
There are two things about my answer to keep in mind. First, my Palm has a resistive touch screen. New devices tend to have a capacitive touch screen. A capacitive screen registers screen in a different manner than a resistive one, so I don't know if what I said applies to a capacitive screen. If you don't know which kind you have: On a resistive screen, you can use anything as a stylus, but you cannot have multitouch. A capacitive screen responds only to fingers and some special styluses, and has multitouch support. If you think you have a capacitive screen, you can just put any sheet of plastic on it without gluing; an inkjet transparency film should do the trick. Try touching through it and see if it works. If yes, a filter should work too.
The second thing to remember: As I've never used an actual glare filter, I can't tell you if it has any positive effect at all.