Don't have a game room per se -- mostly just a room with a workbench and some games, and my large collection of books.
I put wheels on a fairly tall wooden cabinet I got from the dump shop with CRT, VCR, radio and audio amp on top, before promptly blowing my speakers up (old school technics amp, less than stellar speakers, children of the grave intro such that the first beats were almost too loud... was never going to end well) and wiring in surround sound all around my bed and thus rendering the wheels pointless for the time being. Have a wii (I got it for next to nothing one day) and GC on the main house TV as well. Before that it meant I could play in bed or wheel it out into the room and play with friends on chairs. Have a projector and screen as well but have not really used that. The wheely stand is mostly for the older stuff as it lacks even composite in (RF only, SCART being provided by the VCR) but I will probably change that before too terribly long.
Most of my games are on a shelf on the stairs into here, and while some are N64 cartridges most are disc based games.
I put my 360 onto my main PC monitor (had a spare HDMI in) so there is that too. Handhelds are handhelds.
For the most part it depends upon the space you have, if that space has other uses, how many consoles you plan to have in it (one, up to about 5, more than 5, and with emulation being what it is each of those are viable for various things with more consoles making things rather more tricky), whether you want to do retro and CRT (to say nothing of the size of said CRT -- you can still find a lovely 50 inch beauty or two out there) or are content with some kind of converter and HDMI in/just consoles with HDMI out, whether you plan for it to also be a TV/film watching space, whether you collect dolls (action figures, skylanders, disney whatever, amiibos, statues... all the same thing) and other ephemera, if doing old school or in general then what goes for wired controllers (extensions can be hard to find these days), whether one of those devices also happens to be a PC, if there is a PC is it your main PC, whether you care to run a long HDMI cable or something from the PC in a cupboard/switch into the TV if you are going that way, do you need to be wired for sound and a bunch of other things.