Real Time Strategy(RTS)
Real time Strategy games revolve around base building, managing resources while commanding units around the battlefield.
Notable Games:
Dune 2
Command & Conquer Series(Minus CNC 4)
Total Annihilation
Supreme Commander
StarCraft 1/2
Warcraft franchise
Company of Heroes Series
Warhammer 40k Dawn of War Series
Real Time Tactics(RTT)
Real Time Tactics games revolve around the command of squads and platoons rather than individual units. Gameplay usually focuses on unit combat, tactics, and strategies as well as exploitation of the terrain rather than base building and logistics.
Notable Games:
World in Conflict
Wargame: European Escalation, Airland Battle, Red Dragon
Total War
Men of War
Tactical Wargame
Basically the turn based version of an RTT. These games usually modeled after table top wargames.
Notable Games:
Combat Mission
Advanced Squad Leader
Tactical Squad Based Game
Tactical Squad based games can be in either real time or turn based. Gameplay revolves around command a team of individual soldiers.
Notable Games:
X-Com series
Fallout Tactics(rpg-ish)
Wasteland 2(also an rpg)
Jagged Alliance
Commandos series
Grand Strategies
Grand Strategy games put the player in full control of a single country. Players must interact with other nations as well as manage their country through times of war and peace.
Notable Games:
Europa series
Hearts of Iron series
Supreme Ruler
Crusader Kings 1/2
Victoria 2
Turn Based
Chess
4x Strategy Games
Similar to grand strategy games, revolves around expanish, exploration, extermination, and exploitation. Can be real time or turn based.
Notable games:
Civilization series
Master of Orion
Endless Space
Endless Legend
Sins of Solar Empire
Galactic Civilizations
Space Empires
Note some genres may blend into each other.