We have a recessed shower light fixture and the cover is melted (thank you previous owners...). But I can't figure out what this thing is called or where I can get a replacement.
I've attached a few photos of the cover and the housing.
It's a recessed (canned) light cover (but I'm guessing you probably already knew that).
As "ppumkin" suggests in above comment, try to see if you can find a manufactures name (& model number) on the actual light fixture. Having such information to hand will greatly help you in tracking down an appropriate replacement cover.
Also you might want to check the bulb (Wattage & type) that is currently in there, as it really shouldn't have done such damage to the light cover.
Nowadays you can get compact fluorescent bulbs specifically for recessed lighting, or if money isn't an issue, look into available LED lights for use in recessed lighting.