Or if you do, don't use the glasses the hotel leaves out for you by the sink. According to this video, several hotel housekeepers were caught on hidden video just spraying the dirty glasses with some sort of cleaner (clearly labeled "do not drink") then rinsing and putting them back for the next guest. One segment shows a housekeeper rinsing the glasses, then sniffing a dirty washcloth and, since it must have smelled clean enough, using it to wipe the glasses dry.
It doesn't say for sure, but I'm guessing the plastic cups wrapped in plastic are OK. I'm glad I bring my own recyclable water bottle to drink from in my room, though. Ew. (Thanks to Peggie for the link.)