I just bought Crusader Kings 2 the other day. I believe the genre this game belongs to is called "grand strategy." Most complex strategy game I've ever played. Crusader Kings 2 itself is kind of like a mix between strategy and RPG, where you have to shape your dynasty. There's also a Game of Thrones mod for it set in Westeros that looks pretty good, but I haven't played it yet.
+1 on CK2, and add Victoria 2 (Vic2 has the typical spammy popup problem with Paradox, and has a tendency toward realism in hegemony, which makes it difficult to do anything unless you're the UK, or able to defeat the UK. CK2 is fairly good about keeping the spam down.).
Civ5's latest Brave New World expansion makes it much more playable (diplomacy AI appears better, but it's still pretty random-seeming), but it's still full of snore-inducing micromanagement, and now there're more pointless popups like "Hey, I heard you like Germany. I like Germany, too." or "Hey, I heard you didn't want to ban clams. I am scripted to also currently dislike having clams banned. I don't like citrus, though. Fuck citrus."
Rome:Total War 2 is coming out this year, but I always get excited, then disappointed by CA. They still haven't figured out combat AI, especially in fort battles (it's better in STW2 than previous attempts, though, so maybe on the right track). If you do a Total War, the farther back they go, the better the mods tend to be at correcting problems in vanilla. SC2, SC, and WC3 all still hold up very well, and C&C & AoE II. If you're into WC3, the DotA map ended up being its own standalone game, and I think there's even a DotA 2, now.
Oh -- you might want to try Sins of a Solar Empire if you haven't. Quirky Stardock product... Strategy's a broad category, though... covers tons of genres, given most games are multi-genre. If you're into a more casual sim kind of strategy, you have Tropico 4 (don't recall if it has MP support, though). There's the new XCOM. You might want to try something like Capitalism II (there's a new Capitalism Labs, which is basically an updated Capitalism II with more features and bugs). There's Wall Street Raider (mostly non-graphical corporation sim with an unreasonable level of depth and complexity on the scale of Dwarf Fortress).
