Power adapters (a.k.a. wall transformers or wall-warts) plug into a wall outlet and supply power to your pedals, synthesizers, and accessories.

When a wall wart burns out or gets lost you can often substitute a generic replacement but you have to know THESE FOUR THINGS:

This photo shows a "coax" plug (short for coaxial).  Coax plugs are commonly used on adapter cables.

They have two metal contacts, a center socket and an outer barrel, separated by a black insulator.

DC Outputs can have either their positive or their negative terminal connected to the center contact.

This is the symbol for a center-negative connector.  A center-positive connector would have the plus and minus signs reversed.

A backwards polarity can damage your gear so be sure the polarity pictured on the adapter matches the polarity pictured on your gear. 

If you're comfortable repairing electrical cables, you can reverse the polarity of a power adapter.  With the wall wart out of the wall, cut the 2-wire coax cord somewhere in the middle.  Then reconnect the wires in reverse.  Use solder and heat shrink tubing if possible.

Like the plugs, coax jacks have 2 metal contacts:  a center pin and an outer spring.

The pin of the jack must fit snugly into the center socket of the plug.

Common pin diameters are 2.1 mm and 2.5 mm.   Barrel diameters also vary so, if you can, take your device with you when you shop for an adapter, making sure its plug fits the device without wobbling.

In some older gear, 1/8" phone plugs and jacks are used instead of co-ax connectors.

Wall adapters can only supply a limited amount of current.  The adapter will overheat and fail if it can't supply all the current your gear needs to operate.  Make sure your replacement adapter can supply at least as much current as the original adapter.

The current rating is listed on the adapter in amps (A) or milliamps (mA).  Fuzz boxes can draw as little as 10  mA of current while chorus and delay pedals can draw several hundred milliamps.  Portable keyboards and synthesizers can draw as much as 1500 mA (1.5 A) or more.

Adapters are designed to output their rated current at their rated voltage.  If more current is drawn, the voltage will sag.  If less current is drawn, the voltage will rise.  For example, the output voltage of a 9 V adapter with nothing connected to it could measure up to 12 V.

The same is true for batteries.  An old fuzz box, for example, might sound better with a carbon-zinc battery installed than with a more modern, alkaline battery.  Alkaline batteries have a higher current rating and so their voltage might not sag to the preferred level.

Also available are "universal" wall adapters like those shown below.  With them, you can select various output voltages, either polarity, and a variety of plug types and pin sizes.