Here are some websites that I think are worth checking out. It may be lacking at the moment, but I'm bound to add more in the future.
A Tyrian fansite that has downloads of all versions of the game!
A huge archive of Doom wads. I highly recommend checking this out if you're a fan of Doom.
Legacy 3D Realms Site
The old version of 3D Realms' site. It has tons of freeware games available to download and other goodies.
A good site to visit if you're a fan of the Commodore 64.
Lemon 64's sister site, for the Amiga series of computers.
The Mod Archive
A massive archive of old school tracker music.
Nathan's Toasty Technology Page
Most known for being the home of IE is evil, but a very interesting site besides that.
The Most Officialest SkiFree Home Page!
A site hosted by the creator of SkiFree.
The NES Files
It's hard to get any Nintendo ROMs these days, but here's a good one for NES games.
A great site that has backups of plenty of old operating systems and other software.