Despite my 10+ years on BYOND, I've never actually played Space Station 13.
I have, however been playing another game I could make a topic about...
I should probably give it a try sometime, huh?
Allow me to shed some more light on what Space Station 13 actually is than provided in the OP. (Seriously, I keep trying to make sense of it and all I receive in return is frustration and aneurysms.)
Space Station 13 is a sci-fi simulation/roleplaying/mafia-type game where players take the role of various crew members on the eponymous space station, a deep space research facility owned by Nanotrasen, a morally bankrupt megacorporation, made to study the effects of the newfound "plasma" element. The crew's goal is mainly to keep things running smoothly and to do their respective jobs depending on what role they are assigned; Engineers need to keep the station intact and powered, Medbay needs to heal wounded crewmembers and clone dead ones, Security needs to keep the order, fend off threats to the station and crack down on subversive elements, etc.
That's not all there is to it, though. Depending on the gamemode, some of the crew members on the station may be traitors, agents of the villainous Syndicate that have a bone to pick with Nanotrasen, and work against the station crew to complete their own goal (usually in secret, although there's nothing stopping you from being loud apart from security wanting to cave your skull in with a stun baton). Alternatively, there might be a number of alien changelings (reminiscent of The Thing) on the station, or the station could be under attack and face the threat of destruction by Syndicate Operatives, or the Station AI could be malfunctioning and want to kill everyone on board... you get the idea.
Add in a couple of other miscellaneous elements (what kind of corporation hires a clown on a high-tech space station anyway?) and events (random meteor showers, radiation belts), and the result is a station that will usually fall into chaos in a myriad different ways in the course of a single round. The goal is mainly to survive, keep the station together for as long as possible, or escape if it's going to hell in a handbasket.
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Now, that's a generic description of the game. How the game is actually played varies
very, very much depending on what servers you play them on.
Goonstation is very much a chaotic mess, with very little emphasis on serious roleplay and more emphasis on the mafia elements and random chaos. Something Awful was responsible for resurrecting the previously dead SS13 and is also responsible for much of its current image and the various jokes and memes that have surfaced around the game. Play on this server if you just want to steal someone's segway and taunt security whilst playing saxophones or making fart noises.
TGStation (and recently, its close cousin NTStation) originally spawned from 4chan's /tg/ board, but has since lost pretty much all ties to it. Has a
slightly more serious bent to it, although it's still leaning towards the random fun end of the scale. You're required to make at least a token effort to roleplay on this server (though your character doesn't have to be serious), and the game is played slightly more strait-laced compared to Goon, although it's still pretty silly most of the time. Play on this server if you're tired of greyshirts harassing you in the halls for no reason, but still want to mostly treat it like a game.
Baystation 12, or just Baystation, is firmly planted on the far end of the "lighthearted fun/serious roleplay" scale and isn't budging any time soon. This server plays much less like a mafia game and more like a full fledged roleplaying experience. You're not just playing some random assistant or engineer, you're playing a person with a name, background story, motivations, and skills, and the whole thing is basically "Space Station Job Simulator". Things are much, much less chaotic than on other servers, rounds play up to several hours long and can usually go by without anything of importance happening at all, although things can still become pretty hectic at times. But hey, that's how some folks prefer it. Play on this server if you want to play as something resembling a real person on something resembling a real space station as opposed to "Random Murder Mystery Simulator in Space".
There's more servers out there than that, of course, such as the previously mentioned Paradise Station, /vg/station (from 4chan's /v/ board), or d20station (a second /tg/ server) but those are the main three that I know of, and I don't really have much to say about the others.