I just moved the Quake 1.06 shareware to Download Central. Quake was one of the last big games to use the shareware concept, which would soon become the realm of hobby programmers. Quake II already had a demo instead. So let me grasp the opportunity to explain the difference between shareware and demos, for as similar as the two concepts sometimes are, a difference exists.
There are, of course, many different types of shareware. In the 80s, authors often just asked for a donation, or they set a time limit how long the software could be used before it had to be registered, using it longer would be a copyright infringement. In the Internet age, it became common to disable some features of a program, which could be unlocked by entering a registration number. The relevant type here is the Apogee model, which was tailor-made for games.
The idea of the Apogee model is that the game is split into episodes, usually three or four. The first episode is freely distributable, the others have to be bought. The games themselves are the same, the executables might even be identical, the full version just has more data. The savegames from the shareware episode will remain functional in the full version, after buying the game a player can continue a started game.
A demo, on the other hand, is a separate program. In the 80s and early 90s, demos usually were non-interactive, Abrams Battle Tank and Battle Chess are examples. Interactive demos became common mostly in the second half of the 90s. 688 Attack Sub is an interesting early example, and it combines both, having two scenarios and a non-interactive demo mode.
An interactive demo can be cut together like a movie trailer, containing a few quests or scenarios which are in the full game as well, but not in direct sequence. Pharaoh is such an example. But it might just as well showcase the game mechanics while giving nothing away from the story. The Fallout demo had a map, location, characters, and plot all of its own. Since demos are often, though not always, released before the full game, they may represent an earlier stage of development and are therefore often quite interesting.
In short: demos are like movie trailers, shareware is like giving the first volume of a set away for free.