Well, PS1 games are CD format, and almost all PS2 games are DVD format. I'm not sure about XBOX, but I believe they are DVD format, as well. Gamecube.... I think DVD as well. So you just need a DVD-ROM to read most videogames.
You can still read the data from GameCube games in a normal DVD-ROM drive. (Haven't you ever noticed that smaller circle in the tray? It's for mini discs like that.)
So anyway, like I said, you'll be able to read them all with a DVD-ROM drive.
Yeah, you can't just play them if you pop them into your computer. Reading the data is one thing, using the data to play the game on your computer is another. Gotta get an emulator. (From what I hear, the emulators for the latest consoles aren't that good.)