Man I should have been there for this goddammiiiiiiiit
On history: In my misspent youth I downloaded every single new video on SDA and TASvideos.org, watched them to completion, deleted the boring ones and kept the good ones. Haven't done that in a long while but I do have some history with the scene. It was mentioned that SDA originally started as a Quake-centric site, and someone said it was basically the beginnings of organized, competitive speedrunning. But from what I understand those beginnings are actually with Compet-N, which was a Doom/2 speedrunning community. I think they still basically hold most Doom/2 records to this day - we are talking about seriously passionate experts here - but I haven't visited the site in ages.
As for speedrunning's popularity, it's directly related to the ease of video use. Early on in interhistory there wasn't a great way to take video footage of a running videogame. Instead, sites distributed demos - ingame recording files that use the game's own software to recreate the recording. (This is where the "demos" in "Speed Demos Archive" comes from.) These files are tiny relative to generic video files, but they require the game itself to run, which obviously limits their popularity. Later on SDA started offering things like mpegs and .movs of speedruns, but this was the pre-streaming era and they were massive direct downloads from their FTP. Easy streaming made speedrun videos popular, like it made all internet video popular.
On PC vs. Console: I agree that a lot of the most popular runs these days are of classic 8- and 16-bit console games, but I think that's just because of general nostalgia and nerd cachet. Speedrunning basically started with PC (Doom and Quake) and continues on in a grand tradition. One of my favorite speedruns ever is Morrowind, which when I was current on these things had like a 14 minute record based on abusing alchemy and magic items. I'm sure it's much lower now. Also the Half-Life 2 speedruns do amazing things with the gravity gun and Source physics to produce truly outrageous speeds and jumps.
On the collaborative community: Though speedrunners are ostensibly in "competition" in that they try to beat each other's times, I think the collaborative spirit comes with the basic desire that drives all speedrunners: The Perfect Run. It's a kind of Platonic ideal, and anything they can contribute towards that perfection is something worth doing, even if ultimately they are not the player that pulls the run off.
In my mind there are basically two kinds of speedrunners: the perfectionists and the collectors. Perfectionists are ones who run popular, well-run games over and over, looking for new glitches and strats, anything to shave off a few seconds and get ever closer to The Perfect Run. By contrast, the collector faction wants there to be a solid speedrun of as many games as possible - these are the types that seek out obscure, infamous, or otherwise curious games, which is why the SDA database has swelled. But both share a kind of teleological mindset where work is constantly done to eventually produce a gleaming example of perfection, whether it be a single perfect run or the perfection of every game ever made being run. Actually speedrunning in general is an interesting example of the OCD tendencies videogames evoke taken to extremes.
On TASes: Some of my favorite TASes are labelled "playarounds," where the goal is not exactly the best time but rather ridiculous feats of superhuman exploitation. Apol mentioned the Mortal Kombat glitch/combo fest (this is actually pretty common for fighting games, which are otherwise fairly boring for pure speedruns), the funny correct-answer Brain Training drawings, and the hilarious Family Feud phrases. I think my favorite in this category is the Mega Man X1/2/3/4 speedrun, which plays all four games simultaneously using ONE input. In other words, one controller controls all four games. It's almost impossible to watch, but it's an exercise in what can be done with dead input frames. Also you might take it as a snide comment on the similarity of Mega Man games but why would you be a jerk like that?_________________Let's Play, starring me.