Most Reprap electronics use 12V DC ranging from 5A-20A.
The motors plus single hotend take up to 5A or so, a heated bed typically takes 5A-15A. So for a standard setup with heated bed, look to about 18-20A total which is about 220-240W at 12V. For some setups you might be able to use less power.
There are several different options of power supply that can be used and are commonly available.
Standard ATX PSUs
These provide +12V, +5V, +3.3V and +5V standby (as well as -12V, but at a low current).
ATX PSUs are commonly used to power RepRaps. Some RepRap controller electronics have connectors for direct connection to the PSU Molex connectors, for other electronics the connectors will need to be cut and connection to stripped wires made. Some electronics (e.g. RAMPS) can use the Power-On signal to wake up the PSU from standby.
ATX PSUs vary a lot in quality and usually need to be oversized, as many cannot provide the rated power for a typical RepRap usage. A typical ATX PSU can usually provide about half its rated power on the +12V rail, so it is best to use a power supply rated 400W or above, and check what current the +12V rail(s) is(are) rated for. Otherwise the PSU will struggle to maintain a stable 12V output. This is because standard ATX PSU’s generally supply not only +12V, but also +5V and +3.3V at high currents. RAMPS controllers only use the +12V (at up to 16A) and eventually +5V (at less than 500mA) for servos.
Good ATX PSUs have thermal overload protection and shut down safely on overload, but again, poor quality ones may not do so before overheating.
To use an ATX PSU with RepRap electronics you need to connect "PS_ON" to the corresponding pin. It is also possible to short it to the ground, this makes PSU start as soon as it is plugged, but it is not recommnded, this would not give you control over PSU. Also depending on the particular ATX PSU model used, a dummy load on the 5V rail is required to get good regulation of the 12V rail.
See here for more details:
There are also PSUs taken from servers which can be used. These usually provide 12V only, but a LOT of current (32A), and quite cheap.
They usually have a proprietary connector designed for rack mount systems, so need some custom wiring depending on the model.
Here are instructions for HP PS-3381-1C1 400W PSUs http://www.rcgroups.com/forums/showthread.php?t=358340
General purpose power bricks
These come in a variety of types up to around 240W, for normal use select a 12V 220W version. Also available are 24V versions.
They often come with a barrel type or 4 pin connector. The 4 pin connector is sometimes called "mini-DIN" or "power DIN", but is not a standard DIN connector.
Also the pin assignments can vary, but for most boards you will need to cut the connector off or make an adaptor.
Here are instructions for converting a Dell laptop charger : http://lbmakersociety.org/2012/12/creating-hacking-a-reprap-power-supply-for-ramps/
XBOX 360 PSU
There are several versions, choose the 203W version. Note that the power may be insufficient for some heated beds. The PSU will shutdown if an overload occurs.
These provide 12V, 5V and 5V standby and power on input.
The XBOX power connector can be cut off and connections made to stripped wire, or make an adaptor with an XBOX power socket (sold as spares on eBay etc).
How to use XBOX 360 PSU with Reprap : http://www.thingiverse.com/thing:13980
OEM type PSU
Note: before you decide to use an OEM type PSU (a.k.a. LED strip PSU) please take a look at the comparison between LED strip PSUs and ATX PSUs in the section Choosing a Power Supply for your RepRap - LED strip PSUs or ATX PSUs and the discussion tab in the same page.
These are designed to be wired into custom installations. For this reason, there is no cord or plug panel included with the PSU. You can cut a power cord in half and wire it directly to the mains connections, or install a plug. In the US, IEC320 C14 plug connections are common, but use your preferred standard.
OEM PSU's have exposed mains connections which should be enclosed to prevent access. It is recommended to get closed frame types, but these still have exposed mains connections. There are also several printable enclosures on Thingiverse, such as NewtonRob's 12v Power Supply Cover with standard cord and switch.
They come in several versions, 12V or 24V and up to 400W. The input voltage is usually universal, switchable between 110V and 220V, or sometimes fixed 110V or 220V. Check that it is compatible with your mains voltage before purchasing.
Controlling the PSU
In order to save power and prevent possible fire hazards you can control the PSU. ATX PSUs are controlled by PS_ON Pin, and the rest should be controlled with a relay. When using relay you would also need a seprate 5V logic PSU to be always on. Having a Realay or PS_ON pin connected enables most firmwares to utilize M80 and M81 commands.
You can find PSUs about everywhere you can find electronics parts.