An arcade game is a coin operated video game machine. These have been around for decades in one form or another, although they peaked in popularity back in 1983.
There have been literally thousands of different arcade games made over the years, from Computer Space (the first real arcade game), to the latest Super Ultra Capcom Vs. Mortal Kombat Special Rainbow Hyper Fighting Edition 3.
Arcade games come in four basic form factors; upright (a free standing machine ranging from 4.5 to 6 feet in height), cocktail (a small table unit with a screen inside the table top), cockpit (a sitdown style cabinet), and bartop (small machine, usually touchscreen, meant to be set on a table or bar). There have been a few machines that have defied the normal form factors (such as Time Traveller, a standup cocktail, and several sports related titles), but the vast majority of games fall into those four groups.
Arcade games are often converted into the latest titles, which is why you rarely see older games in your local arcade. That Neo Geo machine you are playing on was probably 6 other games between the time it rolled out of the factory as an Asteroids back in 1979, and now when you are putting in your quarters.
Most modern arcade games conform to the JAMMA standard, which means you can take your Final Fight boards and plug them into a Moonwalker, Streetfighter II, or any one of hundreds of other game cabinets. This standard was made to cut down on the senseless rewiring of cabinets for every new game. Even some gambling machines now use the JAMMA standard.
Controls are varied, although joysticks, trackballs, and pushbuttons are most common. These are industry standard parts in most cases. Meaning that you can replace your Double Dragon joysticks with a set out of a Clutch Hitter with no ill effects.
The vast majority of games use a standard color arcade monitor, and produce graphics in the same manner as your computer. But a few older games use vector graphics, and games with laserdisc generated graphics are not entirely unknown.
Older arcade games are often sold on the secondary market, and can be purchased for rather reasonable prices for home use (you can probably get two full sized arcade games in nice shape for the same price as a Playstation 2 with 2 games).
There are thousands of individual games that have been written up here on E2, it wouldn't even be possible to list them all in this node. But I will list some more nodes about arcade games in general, and arcade terms and technology.
Arcade Related Nodes
Feel free to msg me if I missed something.
Pinball machines and other electromechanical games are somewhat related to arcade games (they came first). But collectors usually consider them to be a separate category.