Usually an old VideoGame. One that is remembered by hoards of pasty faced geeks with fondness. I guess you could also include the really good modern games such as Q3 and the wonderful Half-Life too.
I would consider Quake to be a classic. Quake III isn't even close.
There are a few key terms which differentiate periods of VideoGameDevelopment. These are common terms, and the exact dates vary somewhat.
- classic - generally refers to vector-graphic games, like Asteroids.
- classic arcade - pushes forward into the first primitive sprite-based games, like Joust, PacMan, DonkeyKong, and the like. Yes, classic games are already arcade-only.
- old school - almost interchangeable with "original Nintendo game" or other game of the mid-80s. Once millions of people were playing Video Games at home, a precedent was set. With this era, the classic Video Game became well-defined as a period.
- older - any primitive 3D game with flat-shaded polygons falls here. PlayStation games, N64 games, and 3D PC games.
- Video Game - whatever is currently in vogue with a large player base. Grand Theft Auto is a current example.
- Next-Gen - a game which is planned for release in the next technology-cycle, or a game which is thought to be indicative of trends which will carry over into the next technology-cycle.
Classic games must pass the same test as any classic. There's a reason why a Mustang is a classic but a Pinto isn't.
Cars are one of the poorest examples you can give, because there really are "hard definitions" of classic: for example, see http://www.dot10.state.pa.us/pdotforms/fact_sheets/fs-ant.pdf. Legally, a Pinto is a classic. On the other hand, I don't know of any video game aficionado who wouldn't consider, for example, MULE or Civilization or Balance of Power to be a "classic".