Dig Dug was an old arcade game released way back in 1982 (this title was sold simultaneously by both Namco and Atari Games). There were two sequels, Dig Dug II (arcade version is impossible to find), and Mr. Driller (who is Dig Dug's son, this title is available in the form of arcade JAMMA boards, or for most newer console systems).
It appears that the gameplay of Dig Dug has already been adequately described by 65535, so I have little to say on that matter, except for one minor correction. Level 256 starts with a "Pooka" directly over your character, he kills you before you can move. No matter how many men you have left, you will simply be killed over and over again upon reaching that stage. There is no way to avoid this unless you are playing on an emulator that allows you to cheat.
The Machine
The upright Dig Dug machine came in the same cabinet as several other Atari titles (such as Kangaroo and Centipede). The control panel had a single 4-Way joystick mounted centrally, with "pump" buttons on either side of it. The machine was decorated mostly with cartoon graphics showing scenes from the game, superimposed over a yellow background.
There was also a cocktail version. It had two control panels (one on each end). Each panel had a "Pump" button on either side of the joystick, so left handed players can play equally well. This model used a 13" monitor (as opposed to the standard 19" in the upright), and the game image flipped for each players turn. The top glass is decorated with some cutesy pictures of Fygar, Pooka and Dig Dug.
A Dig Dug boardset will plug right into a Galaga cabinet, although you have to switch Galaga's 2-Way joystick for a four way, and run the 2 extra wires for up and down from the wiring harness, but Galaga plays fine with a 4-Way, so this is a nice and easy project to have two classic games in a single cabinet.
Where to play
Dig Dug has been ported to most video game consoles from the 1980s (Atari 2600, Nintendo Entertainment System, etc), so it should not be too hard to find a copy. You can also play this title under MAME on your personal computer.
This is an excellent title for your arcade game collection. Although it can be expensive. If you are considering purchasing a Dig Dug machine, then you might want to look at buying a Namco Classic Collection Volume 2 machine. It will cost a little more, but you will be purchasing a game that is 14 years newer (which means it will last you 14 years longer), and it contains Pac-Man, Rally-X, and New Rally-X in addition to Dig Dug (this machine features both the original versions, and new updated versions).
Beware of bootleg versions, which will usually be labeled "Zig Zag", they are problematic at best.