Apparently, hotels don't properly wash the glasses in the rooms. The Fox I-Team used spy-cams and of the 3 hotels they checked, all of them were pretty gross. The housekeeper would just put them in the dirty sink and spray them with glass cleaner, wipe them out and put them back - maybe using your dirty washcloth, and wearing the gloves she used to clean the toilet 2 minutes earlier!
This is a definite health code violation, and consequently the glasses may harbor many different kinds of germs.
It may not happen across the board, but I guess you should bring your own cup or drink from the bottle! Something to think about!