Old books are kept in a library. Old movies are kept in archives. But where are old video games kept?
Don't sweat it: they're kept safe and sound. Or, at least, the ones developed and/or published by some of the industry's biggest names are are, a great feature on Gamasutra finding out the archiving and storage policies for all three platform holders and some of the world's top third-party publishers.
Here's what Microsoft do:
Microsoft preserves (archives) multiple copies of each game title distributed by Microsoft as well as the source code, hardware and most of the production materials (e.g. game trailers, print advertisements, character designs, etc.). All our collections are stored in humidity and temperature-controlled environments in multiple onsite and offsite locations.
Nintendo is less specific, but with the Virtual Console stuffed with old games, that's all the proof you need its classics are still in good working order.
Nintendo keeps a wealth of materials related to its past games, up to and including even original design sketches and documents. Preserving these games lets us reintroduce them to new players while giving older gamers a chance to relive their glory days.
Sony, meanwhile, does its best considering the size of its games library and worldwide development staff:
Regarding source codes and game assets, we manage storing them per region, and depending on the region, we use off-site storage or on-site servers to store the data. IT group and QA group take an active role archiving game codes and assets developed by internal studios in a consistent way, but archiving externally developed titles are varied depending on contracts.
Capcom does have a procedure for preserving their code. However, these procedures, like many other Japanese publishers were not instituted until around the 16 bit days. I have actually seen massive stacks of dot-matrix printer paper that contained game code on them.
On a side note, I've heard of incidents of old game ROMS from other publishers that have disappeared and are forever lost. I was quite surprised to initially hear this but I was even more shocked when I found out that it is quite common for code for a lot of big name 8-bit titles from other publishers to be gone.
Those quotes are just skimming the surface, as both Microsoft and Sony go to great lengths to outline just what it is they keep, where they keep it and what criteria determines what is kept and what's binned. There are also a number of reports from other publishers and developers, including Namco Bandai, Gearbox Studios and Sega.
Great reading for history buffs.