
A role playing game is typically a game that is very long and drawn in. There aren't too many RPG's out there that does not require over 20+ hours of your life. Some fine examples of RPG's are Final Fantasy, Dragon Warrior, Breath of Fire, The Elder Scrolls and other many varieties. Typically a RPG involves a group of characters that you need to build up or develop to reach a common end goal. To get to this goal, you will need to strengthen your character by leveling him up or gathering new equipment.
A first person shooter are more popular amongst the multiplayer world than the single player world. Albeit, some single player FPS games have captured our attention very well. Some fine examples of a FPS game would be Half-Life, Counter-Strike, Doom, Castle Wolfenstein and many other types. A first person shooter puts you into the role of a single character toting many weapons and the common goal of reaching the end, escaping doom and all that fun stuff. When playing in a multiplayer game, you can play in a FFA (Free For All), Team game or any other varieties.
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, Age of Empires, Command and Conquer and many other varieties of games as well.
The sports genre are typically those sports which you can play in real life. Sports like, skateboarding, snow boarding, 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 many other varieties of games as well.
Racing games revolve around one of the following: stunts, speed, tricks, collisions, or any of the above together. Off-road Racing and Need for Speed are fine examples. It can be trucks, snowboards, skateboarding, dune buggies, sports cars. Some good examples of games like this would be Need for Speed, Moto Racer, Off-road Racing and other titles as well.
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!