Given that being prone means you are lying on the ground (Player’s Handbook, page 311), who can be prone? Can oozes be prone? What about creatures with no limbs like snakes? What about incorporeal creatures?
Anybody can be “prone.” Creatures that use limbs for locomotion can use a free action to drop prone and must use a move action to stand up again. Something with no motive limbs, such as a snake, can go prone or “stand up” as a free action. Such creatures might want to become prone to gain an Armor Class bonus against ranged attacks. (Although giving something like a gelatinous cube that option defies common sense and should not be allowed.) Officially, there’s an attack of opportunity any time a creature stands up. The Sage, however, heartily recommends no attack of opportunity when a snake or similar creature “stands up.”