Sometimes copyright owners decide to release games for free themselves. Companies like Id Software, makers of the popular "Doom" and "Quake" franchises, have been known to release the source code of their older games to the public. Activision, Apogee and Sierra have released old titles as freeware. The company Parallax Software released the source code of their game Descent in 1997. The website Remain in Play hosts a lot of games that have been released by their owners in this way.
And these days, lots of companies are reviving old titles for smartphones and newer gaming consoles, for a price, of course. The 1993 game "Myst" was ported and re-released to smartphones and modern gaming consoles in 2009. Xbox Live Arcade includes lots of classic game downloads, and PlayStation Network includes many of PlayStation's older games.
A number of other companies have made mobile versions of their old games. Activision released an anthology of their Atari 2600 games that includes "Pitfall," "River Raid" and "Kaboom," and released a "Lost Adventures of Infocom" app that allows you to purchase Infocom text based games. Atari has similarly made their games available for smartphones and tablets, including "Centipede," "Asteroids," "Missile Command," "Yar's Revenge" and many others. The games of Bandai Namco ("Pac-Man"), Capcom ("Street Fighter II" and "Ghosts 'n Goblins"), Midway ("Joust," "Defender" and "Rampage"), Sega ("Sonic the Hedgehog") and lots of others are available for mobile devices, as well.
The current owner of Atari lets you play revamped versions of the company's old games online at Atari.com/arcade for free. But if you'd really rather play the original versions with an old-school controller, the Atari Flashback game console was created solely for playing old Atari 2600 games, which are preinstalled in the console (no cartridges required).
GOG.com gets the rights to and sells downloads of older PC and Mac games at reasonable prices. Steam is also a good source to purchase downloads of games you might think are abandonware but are still available for official sale on newer platforms.
And you can, of course, go really old-school and purchase working vintage computers, gaming consoles and games via eBay and other online avenues, or pull them out of your own closet and test them out. A lot of them are still out there for now. But eventually, all old hardware and physical media will go the way of the dodo bird. And when that happens, abandonware or similar sites might be the only way to relive our game-riddled childhoods.