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!

/idgames Archive
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.

Lemon 64
A good site to visit if you're a fan of the Commodore 64.

Lemon Amiga
Lemon 64's sister site, for the Amiga series of computers.

Macintosh Garden
A site with a wealth of software for Macintosh systems. Very handy if you have an old Macintosh.
If you're a fan of the Marathon trilogy, this is a site well worth checking out.

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.

A great site that has backups of plenty of old operating systems and other software.