Here I will try to explain some game genres, more to come.
Role Playing Game (RPG):
Typically a long and drawn in game, it may require more that 20 hours to complete (at best). Some examples include for JRPG (Japanese): Final Fantasy series, Secret of Mana, Breath of Fire. And some WRPG(Western) Mass Effect.
Usually you will have a group of characters with different classes (Thief, Mage, Warrior, Healer etc.) and you have a main quest line. During gaming you try to build up character skills, gain different items and equipment, and also do side quests.
First Person Shooters (FPS):
More popular amongst multiplayer world, while some single player FPS games capture also attention.
Some fine examples include Half-Life, Doom, Quake, Halo. You are in control of your character usually from FPS view, and have different weapons killing enemies. Multiplayer example includes Free For All (FFA), Deathmatch (DM) or Capture the flag (CTF).
Real Time Strategy (RTS):
The role of a real time strategy game is to put the strategic part of your mind into the views of a fast paced environment. Typing your goal in a RTS game would be to defeat the opposing army with an army of yours that you have to build up by getting resources. Fine examples of RTS games would be Starcraft, Warcraft, Total Annihilation, Command and Conquer and many other varieties of games as well.
Sports Games:
The sports genre typically denotes those sports at which you can play in real life. Sports like, skateboarding, snowboarding, tennis, basketball, football and likewise. They feature real life pro teams and they put you into the game so to speak.. Some good examples of games like this would be Madden NFL, Cool Boarders, NBA Slam, and many others such as PGA Tour Golf, Tiger Woods Golf, Brunswick Bowling.. As you can see the sports topic and genre revolves around the biggest series of games out there.
Racing Games:
Typically they revolve around one of the following: stunts, speed, tricks, collisions, or any of the above together. Game can include trucks, snowboards, skateboarding, dune buggies, sports cars. Some games in this topic could be Need for Speed, Dirt.
Puzzlers: Puzzle games are another variety that is very popular. Your typical puzzle game can include everything from chess and checkers to your lonely Marble Madness. This genre is way too undefined to actually write a source for. Let's just say, if it involves your brain in a puzzle type environment, it's a puzzler!
Of course there are other types, as Pinball games etc..
