The gameplay of Robotron: 2084 has already been covered very well, so I am going to concentrate on providing a little information on the arcade cabinet, and on the hardware that the game runs on.
The Hardware
Robotron runs on the Williams Classic platform which also runs Joust, Stargate, Splat, Sinistar, and Bubbles. All six of these games use nearly identical PCB boards, and several people have successfully rigged Robotron boardsets to run all six titles at once. The game itself runs on two processors, an M6809 (at 1 Mhz), and an M6808 (at .895 Mhz). These processors, along with 12 game ROMs, a sound ROM, and 24 4116 RAM chips (2k each for a total of 48k of RAM, 38k of which is used for the screen buffer), are spread out among a set of four PCBs (printed circuit boards).
The game uses a standard open frame monitor, and runs at a resolution of 304x255. The game can display up to 16 colors at once, but has a 256 color palette (which is why this game has so many color cycling effects).
Robotron requires a special power supply board that provides currents of +12/-12 volts, +5/-5 volts, +27 volts. It also feeds 6.3 volts AC to the marquee light. This board cannot easily be replaced by a standard arcade power supply due to the need for the +27 volt feed (which is nonstandard). Luckily a defective board can be repaired with off the shelf parts.
There were two different ROM revisions for the this game. The original release was known as the "Yellow/Orange label", and sets the game at difficulty 5, and sets the default high score at 131682. This release also called the Quarks "Cubeoids" on the demo screen, and had a bug related to firing directly into the corners of the screen. The second revision was known as the "Blue label" and it fixed the firing bug, turned the difficulty down to 3, renamed the "Cuboids" to their more common name of "Quarks", and jacked up the default high score to 151782. In most games it is more desirable to own the earlier ROM revisions, as the later revisions usually make the game more difficult, and fix any "unlimited lives" tricks that players may have come up with. But with Robotron you are going to want to play the later revision, as the difficulty has actually been decreased (although you can always change it in the game settings anyway).
The Cabinet
Robotron was available in both upright and cocktail format, with the cocktail cabinet being fairly rare. I have been able to locate photos of 3 different upright cabinet styles for this title, although the only common one seems to be the white one (so that is the one I will describe).The alternate cabinets also had different graphics (at least the color scheme was different), and are much more difficult to find replacement graphics for.
The standard Robotron upright was 6'2" tall and featured white sides and a black front. It had painted sideart in the form of a "2084" logo and a few stripes (this is a very simple design, and is easy to repaint if your cabinet happens to be scratched up).
The control panel is covered with a geometric shape design, and has two 8-Way joysticks, and two start buttons. These joysticks are of a peculiar design, but can easily be replaced with a pair of modern joysticks (purchase red ball tops ones, because that is what the originals had).
The games marquee has the "Robotron" logo in a font reminiscent of an early 80s computer. This is superimposed over a triangular design made from shapes and lines. I was able to find photos of four different Robotron marquees, but they all had the same design, only the color scheme was different.
The Robotron cocktail cabinet was finished completely with woodgrain laminate. The only graphics were on the control panels, and the small instruction cards that were placed under the top glass. The players would sit across from each other, and the screen image would flip for each player.
Where to play
You can play Robotron on the Atari 7800, the Atari 5200, or you can also play it on one of several William's Classics compilations that are available for PCs and several modern consoles. Digital Eclipse sells an authorized Macintosh port, that runs well on even the older 68040 machines (this is actually an emulator, and it will play other Williams' games simply by switching the ROM image that the game accesses, although they don't advertise that fact).
Robotron: 2084 is an awesome game to add to your arcade game collection. But it is also one of the most expensive "classic" games out there, with an average price of over $1000 (USD). I would suggest locating an old converted Robotron cabinet, and building one by ordering parts. It will be much cheaper that way.