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.
People like you are the "Savers" of this precious Achievement of Humanity
Quote from Wikipedia:
A book is a medium for recordinginformation in the form of writing or images, typically composed of many pages (made of papyrus, parchment, vellum, or paper) bound together and protected by a cover. The technical term for this physical arrangement is codex (plural, codices). In the history of hand-held physical supports for extended written compositions or records, the codex replaces its immediate predecessor, the scroll. A single sheet in a codex is a leaf, and each side of a leaf is a page.
While I am unlikely to attend a book burning any time soon (at least not without my rifle) this is mostly because not everything is yet available online, computers have massive perks (searching, storage capacity, bookmarks, animations, colours...) but sometimes fingers in an earlier page is good, and it is a cheap hobby if your main subject matter is engineering (especially old school engineering), history, propaganda and old stories where you don't need signed first edition copies of 1700s books or books where the author only because famous after they died.
Anyway presenting the pig sty I seem to live in. Can't be bothered to go take a picture of the gamecube and wii on the main TV (it is a wii and gamecube, plus controllers and a bunch of games I got because the gamecube was a failure and games used to cost nothing before people got a wii and realised they had nothing to do but backwards compatibility was a thing -- it is the standard collection of good first/second party games plus some third party titles because I did not get an xbox until later in the day and it was a good way to play them).
Also I don't love you all enough to unplug the surround sound and rewire it afterwards so pulled the chair out instead. The stuff next to the floor to ceiling bookshelf is supposed to mostly be in the shed but that is full of motorbike parts and more of my tools right now.
My game room's also not done yet. I've made a few blog posts about renovation and how it takes longer, so take my "it'll be done somewhere during the summer" with a grain of salt. But my game room (or "study room", as I'll obviously call it) is under the (sloping) roof, so it'll have plenty of shelf space for my (old) video games, a game system and the lesser played/solo) board games. As well as my desk, obviously.
I don't have a picture to offer right now, but imagine a 3DS in some random guy's hands. That's my game room.
Though we have, shit I lost count, quite a number of consoles in the house, including a new Switch my wife got me for Xmas, I still just enjoy playing on my 3DS for whatever reason. Probably just a matter of time between work and such.