Genre: How do we define games?

All art forms use genre to sub-define themselves; movies, books even television shows all use genre to help consumers choose which product to buy. Gaming itself is built off of several 'core' genres:
First Person Shooters and Third Person Shooters (FPS e.g. Halo, Call of Duty, Gears of War)
Real Time Strategy games (RTS e.g. Starcraft, Age of Empires)
Platformer (e.g. Mario)
Role Playing Game (RPG e.g. Final Fantasy, Zelda [Zelda may be arguable but we'll talk about that tomorrow])

But genre is not a perfect system, and we often see it limit the potential of games. When a producer green-lights a game, they often do it based on genre; if they are producing an FPS and the product is very heavily based on puzzle elements they are less likely to produce that product because they are worried that their core FPS community won't be as interested in that game. That game may have been really fun, and the puzzle elements may have helped the game sell better, but the studio is afraid to cross genre lines. This is why FPS/RPGs are generally not FPS/RPGs but rather FPS with a dash of RPG on the side (Borderlands, Mass Effect 2).