Freeware games are completely and officially free. They might have been free since the beginning, or in some cases, they are paid games that have been declared free by their creators. A game that is distributed as freeware can be freely distributed, downloaded, and played by anyone. It's forbidden to sell or ask users to pay for them. Freeware games are complete, unlike shareware games, which can be freely distributed but must be purchased to get the full content. In some cases, old titles are released for free to promote the release of a new game.
Some old classics like Adventureland and Mystery House are officially freeware, but also Beyond Castle Wolfenstein or the text adventure The Hitchhiker's Guide to the Galaxy, like other Infocom titles. The old RPG Ultima IV: Quest of the Avatar and the revolutionary cinematic platformer Prince of Persia are also free.
Factor5 also released three of their Amiga games for free: the space shooters Katakis and R-Type and the cute platformer B.C. Kid.
Revolution Software released some of their graphic adventures for free, such as Lure of the Temptress and Beneath A Steel Sky. Sports Interactive's football management game Championship Manager: 01/02 is freeware.
Some great strategy games are free, like Star Control II or The Patrician, as well as the famous RTS Command & Conquer.
Bethesda released two episodes of the Elder Scrolls series: The Elder Scrolls: Arena and The Elder Scrolls II: Daggerfall.
Finally, you can play for free the first iconic Grand Theft Auto by DMA/Rockstar North.
There are many other freeware games out there, the list changes often, so stay tuned.