The EPROM (Erasable Programmable Read Only Memory) is a popular variation on the PROM design. These are a PROM that can be erased. You can spot these easily because they will have a little quartz window on top (you can actually see the innards of the chip through this window). These are functionally identical to a PROM, but with the added ability of being reprogrammable.
The little window is there so the chip can be erased if needed. EPROMs are released by exposure to intense Ultraviolet (UV), light. Quartz is used because glass blocks UV light.
The UV light is able to erase the chip because it cause a chemical reaction that basically melts all the little "fuses" in the chip back together causing all the zero bits to become binary ones again. An EPROM chip can be thought of as a bank of thousands of tiny fuses, with blown fuses representing zeroes, and solid fuses representing ones. Although in scientific terms, EPROMS are actually made of transistors; the transistor is held open or closed by the induced field of a charged particle encapsulated in an insulating material above the gate. The UV rays excite the particles allowing them to be charged or discarged despite the insulating material. Garden variety UV light is not enough to erase an EPROM, you need high intensity light with a very close source, at a precise wavelength (2,537 angstroms). Even this specific light takes several minutes to erase the chip. Erasure is usually done with a special "EPROM Erasor", which is designed soley for erasing EPROMs.
EPROMs are usually covered with a small sticker after programming. This is done because sunlight can affect them over long periods of time. It won't erase them fully, but even changing one bit can ruin a chip.
EPROMs are very common on arcade game boards. Most games store all their program code on a bank of several EPROMs. Many games run on identical hardware, and you can change the game simply by burning a new set of EPROMs (you can change Pac-Man to Ms. Pac-Man that way).