As others have posted, Strategy is itself a very broad term, and there are many kinds of strategy games for the pc. There are some of my personal favorites, but it's by no means a "Top X" list, simply because they are different
Starcraft 2 is superb. Plain and simple. The campaign might be the best RTS capaign out there, and the multiplayer... oh the multiplayer. That's where the game truly comes alive. With only a few unit types, simplified resource system, easy controls the game manages to achieve a strategic and tactical depth that is so far unrivaled. Great balance, easy to learn, extremely hard to master, it's a reference game for the genre.
Total War series. Shogun 2 and Rome were my personal favorites, but most of the games of the series follow similar principles, with fairly minor changes between them. All of them however are awesome games, with a fairly unique feel to them. Control massive armies in real time, manage your resources and territory in turn-based gameplay. Another game you really can't miss, since there's nothing really like it.
Civilization V, the latest iteration of the series brings about greatly streamlined gameplay, a greatly improved visual design and is the first game of this otherwise excellent series to be beginner friendly. The old Civ games were awesome, but frankly impenetrable to beginners that made them much less popular than they should have been. It's all turn based, so called Grand Strategy. You start off in the stone age and build up your civilization all the way to the space age, all the while competing with neighbors for resources, technology, territory and fighting randomly spawning barbarians. Another must play.
Heroes of Might and Magic V, again the latest iteration of a great series (and if you like it, you should play 3 and 4 as well, since they are different enough to be fun, while being the same basic game) It's another turn-based game, with overworld maps and instanced fights in the style of old FF games, but with much more strategic depth. Different factions, numerous units with their specific strenghts and weaknesses, heroes, loot. Another must play
Company of Heroes is only loosely a RTS game, since it has more in common with tactics games, but I suppose it has enough strategy blood in it's veins to make the list. It's a great campaign-driven experience, with a fairly unique feel. Another must play.
Warhammer 40k: Dawn of War + the miriad expansions. It's another interesting iteration of the genre with some different gameplay ideas, but with an unmistakable RTS feel to it. Certainly worth a try, especially if you're a fan of the franchise. Just don't make the mistake of thinking about Dawn of War 2 as a strategy game, because it's not (a good game, just not strategy).
Universe at War: Earth Assault is another classic RTS style game with some nicely diverse factions. Nothing especially exciting, but a solid game with a fun campaign.
World in Conflict. Again, nothing groundbreaking or especially noteworthy, but a good game all the same.
Age of Empires was an iconic RTS back in the day, but I'm afraid it hasn't aged particularly well. Give the games a shot if you're really in to the whole strategy thing, because it won't exactly disappoint, but it can't exactly compete with the more modern titles either.
Command and Conquer, a series that is almost unchanged in it's near decade of existence. This is basically what put RTS on the map, and it's newest iterations are ok to play, but frankly you'd likely have more fun with some of the older games. C&C Tiberian Sun, Red Alert 2 and maybe Red Alert 3 are kinda the best titles of the series. Command & Conquer 3: Tiberium Wars is also pretty good. Worth playing mostly because the many extremely similar iterations of C&C make it almost a sub-genre in itself, it's unfortunately not transitioned very well in the modern day.
That's about it off the top of my head, plenty to play anyway. Have Fun
