Perhaps the greatest strategy game ever made.
The game that started out as WarCraft in Space evolved into something even the big Blizz didn't expect, an international juggernaut of Real-Time-Strategy. With it's three totally unique races, epic story, solid gameplay, and endless possibilities on Battle.net, StarCraft is a masterpiece.
This game features the 3 different races - the Terrans (humans), Zerg (creepy aliens), and the Protoss (advanced aliens). Each are totally unique, but are perfectly balanced, and all ooze personality. You gather resources, manage economy/micro management, and blow the enemy up. This has been a staple of RTSs for a while, but the game can go far beyond that with its map editor, and is highly mod-able. It's story mode also stepped outside the RTS boundaries with it's unique missions.
Perhaps its just the fanboy in me speaking, but I think every PC gamer should play this game once. But be warned, it's not easy.