I guess your question is a little general to be answered by the wikipedia article.
There are two ways that PoE works:
1) lower speed ethernet over twisted pair protocols only use two pairs, of the four pairs that exist on an RJ45 connector. So you can "just" run power over the extra wires.
2) Ethernet uses a high-speed AC, transformer-coupled signal. You can run a DC level (even in "power" quantities) over the same wires without interfering with the signal.
(wikipedia will describe the details of how this is done without frying your non-PoE equipment, setting fire to your wiring, or putting up with excessive power or voltage losses in the long runs typical of "business" wiring.)
Yes, similar schemes have been applied to other communications lines. Obviously "string extra conductors" works for any protocol (and so PS/2, ADB, USB and firewire conduct significant amounts of power in dedicated conductors, and Apple used to run power through it's "display connection" cable, and etc.) Low power devices used to "steal" power from the voltages present on "standard" rs232 cables, either by virtue of using extra signals that weren't needed, or "parasitically" by using AC coupling for the signal. For example, RS232-based mice didn't have separate power supplies, back in the day. Finally, there's the Dallas/Maxim "one-wire" protocol, that does bi-directional communications over the +V wire of the two wires used to provide power (+V and GND)