I'm going to assume you mean games that really push a PC in a direction consoles can't go.
The Arma series simply cannot be done on consoles. The complexity of the AI and scale of scenarios allowed is just incredible, though it does have some rough edges, mostly related to performance. It's also one of the few games that will use just about every key on your keyboard. Also, very moddable.
The Total War series has been mentioned. As far as real-time strategy goes, Total War is probably the "biggest". Tons of dudes on screen at one time, great graphics, and realistic tactics. It's fairly slow paced, so you have time to actually think about what you're doing. Or just zoom in really close and watch.
Kerbal Space Program is an amazing game all around. Somehow, anything you do in this game is fun. Even crashing and failing really hard. Absolute must-have if you like science/astronomy or sandbox games. Or blowing things up.
If you want a competitive multiplayer strategy game, look into Wargame: Airland Battle. It has over 800 real Cold War-era units; tanks, helicopters, infantry, tank destroyers, AA missile launchers, etc. You name it, they have it, or at least something close to it. It's very focused on combined arms tactics. You can't just throw a massive column of tanks at the enemy and expect to win.
The Men of War series also shares a lot of those traits, but it's a bit slower paced and on a smaller scale. It's also very playable as a single player game.
If you want insane levels of depth in your strategy games, look at Paradox's grand strategy games. Hearts of Iron 3 is my favorite, personally. Europa Universalis 4 came out a few months back, and it's relatively accessible for new players. Generally, these games cover the whole world at some point in history, and you can play as any nation which existed at the time. They are not balanced, and they are not intended to be balanced. For example, Hearts of Iron takes place in World War 2. If you play as Germany, you will have a very different game from someone who plays as Tibet.
The Civilization series has been a staple of PC gaming for decades now.
The same can be said for SimCity, but EA ruined that with the new one. If you want a SimCity game, you want SimCity 4. It is the city building game. It has tons of mods available, and still has a very large community, even though it came out 10 years ago.
Minecraft should definitely be played, or at least be aware of it. I don't think it's really that great of a game, unless you're playing on a server with a bunch of other people, but it's gaming culture at this point. Minecraft references are everywhere.
I'm sure I'm missing something important.