Basic ideas:
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Power requirements
  Power drawn by arcade games (and on power-up)
    1.1 amps per video game is believed average. Samples ranged from 0.8A-1.5A.
    1.5 amps per pinball is believed average, 2 amps when in use.
    [Electrical current information taken from Clay Cowgill.]
    Determine what size circuits you have running into your gameroom.
    Determine which outlets are on what circuits.
    Typical circuit is rated for 15 amps.
    To measure amperage, try a device like Kill A Watt (tm).
      URL: http://www.p3international.com/brochures/P4400.pdf
      Available at Radio Shack and other stores.
  Grounding plugs on games are REQUIRED -- not optional!
    If your games do not have ground plugs, fix them.
  GFCI outlets are certainly not a bad idea.

Game Power Control
  Putting games on the same circuit as light switch causes problems.
    People will (for fun or unknowingly) turn your games off and on.
    Off-and-on power cycling is not good for games.
    If you must, put a cover over the switch, or locate it in an unusual place.
  An X-10 remote control system is EXTREMELY handy for turning on/off games.
    Major cool factor of pointing a remote at the games to turn them on.
    No reaching behind or around games to turn on switches.
    One button can turn on all games on different outlets (load permitting).
    Potential exists (same say exaggerated) of games turning on by themselves.
  Use a surge protector that is designed to be placed under a computer monitor.
    Example: http://www.apc.com/products/family/index.cfm?id=131
    Example: http://accessories.us.dell.com/sna/productdetail.aspx?sku=A0095311&cs=19&c=us&l=en?order_code=DTAFD&DGVCode=SS
    Plug-ins are in the back. On/off controls are in the front.
    Place on top of a game and be able to manually turn several games on/off.
    Cords are hidden behind the unit.

Smoke Alarm
  A very good idea!
  Note that many alarms will not be able to distinguish fog machines from smoke.

Controlled humidity is ideal.
  < 15% very dangerous for electronics.
  40-60% is ideal for human health.
  Per thanador: Too high on cold days can cause condensation on walls/windows
    http://www.aprilaire.com/pdfs/humidifiers_768.pdf
  Reduces dangerous static electricity and damage to electronics.
  Reduces wood rot.

Temperature control 
  Primary danger is heat.
  People, games (electronics), and lights produce heat.
  Cold can make plastics, rubber, and glass brittle (more susceptable to damage).
  Extreme cold can cause condensation inside of the monitor.
  Fans are generally a good idea. Ceiling fans work very well. Can be decorated, too.
  If there isn't a powerful and nearby AC vent, consider a window AC unit for the summer heat.
  
Entry/Exit
  Big enough to fit arcade games through. The larger the better.
  An outside (front) exit, if possible. Makes delivery much easier.
  Lack of steps is a big benefit.

Windows
  No or few windows is generally a good thing.
  Sunroof is completely off-theme.
  Existing windows should be heavily curtained to restrict light.

Upstairs
  Collectors agree that in most situations, weight isn't a problem.
  House conditions vary. Can't guarantee it won't be a problem.
  If building a new house, check w/the builder in advance.
  Main problem is moving games in and out.
  Even more so if stairs have a sharp turn on a landing.

Basement
  Good location for many people.
  Be sure to control moisture and humidity, if an issue.
  A basement that floods is very very bad.
  Moving games in/out can be very difficult.

Detached Structure
  Expensive, but probably quite ideal.
  Needs it own cooling/heating, even when not in use, to protect games.