Some observations on video game music, and why it sounds like it does. (Work in Progress)
The first music generated on a home computer was a rendition of "Fool on the Hill" (Lennon/McCartney) created on the Altair (as the machine had no sound capability, the ingenious method of throwing it into differently timed loops and placing a detuned radio next to it was used) - this was described as the only useful thing that was ever done with an Altair. Jeff Minter (The Yak) later reproduced this feat with a Vic 20. I won't go into Sinclair Spectrum and Commodore 64 (or earlier) music here, as it was generally unlistenable beeping. Someone else can wax lyrical about Manic Miner and Ghostbusters...
Sega Master System / Game Gear: If I recall correctly, does not have any hardware capability to reproduce samples, just simple waves and white noise (as described above). However it was possible to get the machine to produce a very fuzzy rendition of speech (see American Baseball), usually pausing all other operations while this was going on. It was best suited to producing a rough approximation of a ghostly flute sound (best used in Castle of Illusion), and those old-style oriental instruments (as in Shinobi). (Sorry, I forget the exact names, but they always appear on even the simplest multi-instrument synth). Bass was practically nonexistent.
Nintendo Game Boy / NeoGeo Pocket Color: both of these machines used the same battery-friendly sound system. It was capable of producing stereo, and seemingly was a bit easier to do sampled sounds on (witness Faselei! on the NGPC, which stored its entire intro music as a 30 second sample, complete with vocals!). Drums are generally handled by white noise, but the processing power of the NGPC at least allows for fairly complex instrumentation to be synthesised (able to do a slightly squelchy, but listenable rendition of the soundtracks of the arcade games that made up most of its software library). The "fluty" noise that is the hallmark of PCM(?) style sound is slightly meatier than on the Master System (maybe an extra channel or two in there?).
Sega Mega Drive: Aah, now this machine started to give developers some room to play with. A slightly unusual* Yamaha chip was given sound duties on the MD, at last providing some FM synthesis. It was, of course, down to the ingenuity of the developer to make these resources sound like interesting. Rob Hubbard at EA and also the sound guys at Technosoft both discovered that the machine could produce a slightly odd but versatile guitar sound (See, any John Madden game, Thunderforce IV, Mutant League Football, Road Rash), even if it did sometimes sound like ukelele speed metal.
Yuzo Koshiro on the other hand was going through his big techno phase, and used the sample channel for kick drums and vocal stabs while using the PCM channels to create an uncanny rendition of a DX7, almost anything by Roland, or a fantastic synth piano (Streets of Rage, Streets of Rage 2, Story of Thor, Revenge of Shinobi). JVP Productions (now Toejam & Earl Productions) took a little from both columns to create funk tracks using the sample channel as a drum machine (with some handclaps and vinyl scratching in there too) and the PCM channels as a funky bass guitar (Toejam & Earl). The MD traded off overall sound quality for versatility - as a result, most games sound very different, but there are no attempts at orchesteral clarity... which brings us nicely to...
Super Nintendo: If the Mega Drive and SNES were "a bit different" in the graphics department, they were completely at odds when it came to sound. The SNES's sound hardware has the inbuilt capability to handle a bank of compressed samples (you can in fact rip these samples directly from the ROM using modern emulator tools). This of course allowed farty, low-bitrate cries of "Hadoken" in Street Fighter 2, but more importantly allowed composers to allocate as much or as little memory as was necessary to build unique sets of instruments. The result, a rich, broad sound (although with rather ropey sound effects backing it up, IMHO).
Square took this to insane levels, with Final Fantasy 6 and Chrono Trigger both having truly awesome soundtracks (check out the opera scene in FF6 ... genius!). Yuzo Koshiro popped up again to score the memorable Actraiser. Many developers seemed to use the same approach and exactly the same instruments however ... for example Konami, whose Vangelis-like synth strings graced dozens of titles (of which I liked Pop & Twinbee best, but that's just me).
Amiga and Atari ST: Amiga owners were always bragging that their games had better music, which was sadly often true, even though the humble ST was powering most of the chart music of the time, thanks to the wonders of MIDI.
The 32-bit consoles brought in more channels, and started to close the gap between in-game music and prerecorded music (which was at last an option, thanks to the advent of CD drives). However not all game music went the way of CD. Nights on the Sega Saturn is notable for its generative musical score, which has hundreds of variations.
Around this time "proper" musicians started to get in on the act (although those with long memories will remember Frankie Goes To Hollywood, Journey, Bomb The Bass and god knows who else all tried their hands at game music in the 1980's), with Sony's Wipeout having a showcase soundtrack by various popular beat combos. Gran Turismo brought in Ash (for a ridiculous fee as the story goes), EA started tacking the latest pub-singalong drossfest on each new FIFA title... the list was endless.
But Quake was the first** game to actually have an original soundtrack made by a recording artist (Trent Reznor), previous games being content to simply plunder the artists' back catalogues, usually not resulting in music that fits the game very well.
(I've not covered PC games in much depth here, due to the fact it would take a large book to cover 20 years of sound technology and hackery, and the title of this node probably means videogames as in console games anyway... check out oldskool.org for some interesting info though.)
So, as we begin the third millennium, game music is seen as a more legitimate art form than ever before (there's even a game music Grammy) - hopefully soon to be seen in the same (or better) light as movie soundtracks. Although of course a game soundtrack has to deliver much more than the fairly straightforward process of aurally illustrating 90 minutes of linear, passive entertainment.
(Please note that I've probably got some or all of the technical terms wrong in this -- I don't know all that much about old sound hardware I'm afraid. Sorry. Since writing this I've discovered that the distinction between what I've called "samples" and "waves" is less clear cut than I thought.)
* This is why DOS Megadrive emulators, which generally map the sound to the Soundblaster 16 mode of the PC soundcard, never sound quite right.
**AFAIK