Not everyone knows the different types of games that are out there, so in an effort to form a common language that we can all use, I'll run through each game type and provide a very brief history.
Although arcade games had their heydey in the 80's, they are nonetheless very popular. Nothing will ever replace walking into a dark, crowded and noisy arcade gallery, popping a quarter into your favorite machine and playing an old fashioned game of Space Invaders. Arcade style games attempt to simulate the arcade games themselves. There is such a vast number of these things that it's nearly impossible to enumerate them all, but they include clones of Asteroids, Space Invaders, Pac-Man, Missile Command and Galaxian.
Computer based card games simulate a card game (poker, solitaire, etc); the type of game you'd play on a table top with friends, but the program simulates your opponent(s).
Logic games usually simulate some well known logic puzzle like Master Mind or the game where you have put sliding numbered tiles in order inside a box.
Computer based board games simulate some kind of board game you'd play on a table top with friends, like monopoly, Mille Bourne, chess or checkers. The program simulates your opponent.
Once upon a time, when Apple ][, Commodore, and Atari ruled the world, text adventures were the game of choice of `intelligent folk'. They were self contained executables on disks (even casettes). These days we're a bit more sophisticated than that. Now there's usually a data file and an interpreter. The interpreter reads data files and provides the gaming interface. The data file is the actual game, and is often implemented by a scripting language. So for example, you you could have the two Scott Adams datafiles “The Count.dat” and “Voodoo Castle.dat”. To actually play the games, you'd invoke the scottfree interpreter with the name of the datafile you wish to play.
The first adventure game was Adventure (actually “ADVENT”, written on a PDP-1 in 1972). You can play adventure yourself (actually, a descendent); it comes with “bsd games” on most Linux distros.
They became popularized by Scott Adams, who is widely considered to be the father of text adventuring. You can play Scott Adams adventures using scottfree, the game file interpreter written by Alan Cox, and the old data files, which are now shareware and can be download from Scott Adams' website.
Text adventures climaxed in the 80's with Infocom. There are many Infocom interpreters available for Linux; the most popular one being frotz. You still need the data files, and these are all still owned and considered commercial property by Activision.
As computer graphics became easier and more powerful, text adventures gave rise to graphic adventures. The death of interactive fiction more or less coincided with the bankruptcy of Infocom.
Graphical adventures are, at heart, text adventures on steroids. The degree to which they use graphics varies widely. Back in the 80's, they were little more than text adventures which showed a screen of static graphics. When you picked up an item, the background would be redrawn without the item appearing. The canonical example would be the so-called `Hi-Res Adventures' like The Wizard And The Princess. Later on, the sophisticated graphical adventures had your character roaming around the screen, and you could even use a mouse, but the interface remained purely text.
Linux users can play a large number of graphical adventures written by Sierra Online. The older Sierra games used an interpreter named AGI (Adventure Gaming Interface) which can be played using sarien sarien.sourceforge.net. The newer Sierra games (we're talking about the late 80's here) used an interpreter named SCI (Sierrra Creative Interpreter) and can be played using freesci, available at freesci.linuxgames.com.
Next there are the `point and click adventures' which basically have no text interface at all, and often have dynamic graphics, like a cat wandering around the room while you're deciding what to do next. In these games, you point at an object (say, a book) and can choose from a pull-down list of functions. Kind of like object oriented adventuring. :) There aren't many graphical adventures written natively for Linux. The only one I can think of is Hopkins FBI (which happens to be my favorite game for Linux).
Simulations strive to immerse the player behind the controls of something they normally wouldn't have access to. This could be something real like a fighter jet or something imaginary like a mechanized warrior combat unit. In either case, sims strive for realism.
Some sims have little or no strategy. They simply put you in a cockpit to give you the thrill of piloting a plane. Some of them are considerably more complex, and there's often a fine line between sims and strats (see the next section). A good example would be Heavy Gear III or Flight Gear. These days sims and strats are nearly indestinguishable, but a long time ago, sims were all real time while strats were all turn based. This is somewhat awkward for modern day use, since a game like Warcraft which everyone knows as a strat, would be a sim by definition.
Strategy games have their roots in old Avalon type board games like Panzer Leader and old war strategy games published by SSI. Generally, they simulate some kind of scenario. The scenario can be peaceful, like running a successful city or illegal drug selling operation (SimCity or DrugWars). The scenario can also be total all-out war strategy game like Myth II. The types of games usually take a long time to complete and require a lot of brainpower.
Strats can be further divided into two classes: real time and turn based. Real time strats are based on the concept of you-snooze-you-lose. For example, you're managing a city and a fire erupts somewhere. The more time it takes for you mobilize the fire fighters, the more damage the fire does. Turn based strats are more like chess---the computer takes a turn and then the player takes a turn.
What light through yonder window breaks? It must be the flash of the double barreled shotgun! We have a long and twisted history with FPS games which started when id Games released the code for Doom. The code base has forked and merged numerous times. Other previously closed engines opened up, many engines are playable via emulators, many commercial FPS games were released for Linux and there are quite a number of FPS engines which started life as open source projects. Although you may not be able to play your favorite FPS under Linux (Half-Life plays great under winex!) Linux definitely has no deficiency here!
First person shooters are characterized by two things. First, you pretty much blow up everything you see. Second, the action takes place in first person. That is, look through the eyes of the character who's doing all the shooting. You may even see your hands or weapon at the bottom of the screen. Some are set in fantasy (Hexen), others are science fiction (Quake II), and some are set in the present day `real world' (Soldier Of Fortune).
Just like text adventures, FPS fit the engine/datafile format. The engine refers to the actual game itself (Doom, Quake, Heretic2) and plays out the maps and bad guys outlined by the datafile (doom2.wad, pak0.pak, etc). Many FPS games allow people to write their own non-commercial datafile. There are hundreds, even thousands of non-commercial Doom datafiles that you can download for free off the net. Often, companies discard their engines and put them into the open source community so we can hack and improve them. However, the original data files are kept proprietary. To this day, you still have to purchase doom.wad.
Side scrollers are similar to FPS but you view your character as a 2D figure who runs around various screens shooting at things or performing tasks. Examples would be Abuse for Linux and the original Duke Nukem. They don't necessarily have to be violent, like xscavenger, a clone of the old 8-bit game Lode Runner.
Similar to FPS, but you view your character in third person and in 3D. On modern third person shooters you can usually do some really kick-butt maneuvers like Jackie Chan style back flips and side rolls. The canonical example would be Tomb Raider. On the Linux platform, we have Heretic 2 and Heavy Metal FAKK.
Anyone who has played games like Dungeons & Dragons or Call of Cthulhu knows exactly what an RPG is. You play a character, sometimes more than one, characterized by traits (eg strength, dexterity), skills (eg explosives, basket weaving, mechanics) and properties (levels, cash). As you play, the character becomes more powerful and the game adjusts itself accordingly, so instead of fighting orcs, at high levels you start fighting black dragons. The rewards increase correspondingly. At low levels you might get some gold pieces as a reward for winning a battle. At high levels, you might get a magic sword or a kick-butt assault rifle.
RPG's generally have a quest with a well defined ending. In nethack you need to retrieve the amulet of Yendor for your god. In Ultima II, you destroy the evil sorceress Minax. At some point, your character becomes powerful enough that you can `go for it' and try to complete the quest.
The canonical RPG on Linux is Rogue (the ncurses library can be traced back to the screen handling routines that were written for Rogue!) and its infinite variants like Zangband and Nethack (which has infinite variants itself). Some of them are quite complicated and are great feats of programming. There seems to be a deficiency of commercial RPGs on Linux. If you don't count all the rogue variants, there also seems to deficiency of open source RPGs as well.