Everything relying on fast reaction times, involving lots of explosions etc.

Adventure games are usually story-based. The player controls one or more characters who have to solve puzzles in order to get along in the world. Traditionally, Adventure games use text parsers. Later, point & click interfaces became common.

Games which attempt to stimulate the player's brain cells. Unlike Adventure games, there are usually little or not plot and no characters and the puzzles are often of an abstract nature.

Role-Playing Games on the computer are the descendents of pen & paper games like Dungeons & Dragons. The games are often set in a fantasy or futuristic world. Gameplay usually consists of following a plot, involves combat and evolving character attributes and stats.

The problem with the word 'simulation' is that basically all computer games are simulations of sorts. Therefore, in this context, the meaning is restricted to games which let the player fly an aircraft, control a ship or drive another vehicle. Even then, there should be a minimum level of realism to this simulation - otherwise, the game falls into the Action genre.

Games dealing with sports. There are two rough sub-types. On the one hand, there are sports management games, combining the genres of sports and strategy. On the other hand, there are 'sports-action' games.

Tactical and strategic planning. This doesn't necessarily need to be related to war: business management games belong here as well, for example.