Hearts of Iron III

I have played many, many hours of HoI2 and Darkest Hour, and after finally giving HoI3 a shot, I have to say I'm kinda impressed. HoI3 is deeper and more complex than its predecessors (and its successor), and the complexity was (for the most part) added in the right areas.

The research and production was expanded to give you much more freedom in what you research and how you compose your units, for example you might build very fast and mobile light tank + motorized infantry divisions or very tough breakthrough divisions with heavy tanks and artillery.
The supply system was also made much more realistic, your troops don't immediately run out of supplies if they are cut off, however on the other hand you will now have more difficulty supplying your troops if you penetrate deep into enemy territory with poor infrastructure, like what happened historically to the Germans attacking the Soviet Union.
One infamous part of this game is the order-of-battle system, which looks super complicated and intimidating in screenshots. Essentially you have to create your own command structure for your army, brigades are organized into divisions, divisions are attached to an army corps, the army corps is attached to an army, etc. Your units get certain combat bonuses if they are attached into a correctly set-up order of battle. This is not really complicated, but it's a huge pain to constantly keep it updated as you move units out of the range of HQs, then they lose their bonuses, you need to attach them to a different HQ, and so on...

Generally this game is not *that* complicated, I mean, it's more complicated than, say, Europa Universalis, but if you've played a HoI game before, you will get into this quite easily.
So far, I have played and won a full game as Germany and I was somewhat impressed by the AI. My allies Italy and Japan were actually extremely competent and managed to keep the UK off my back while I invaded the Soviet Union, leading to an Axis victory in 1942. I'm not gonna use the word "easy", but I did expect a harder challenge.
One disappointing aspect is the lack of historical events. There are only few events and almost none of them have choices or consequences for your nation. Fortunately there are mods that add even more depth and historical flavor to the game. Overall, this is a sure recommendation if you like wargames or other HoI games.

One thing to note: You will need to install a Large Address Awareness patch for the game, otherwise it won't run stable.