Short answer: None.
Long answer: Games are actually not that complicated. It depends on what you say when you say “games”, but two contenders for the most complex games are 3D games and online games (especially mass online games).
Complication in 3D games comes from taking a model of the world and rendering it in 3D and in order to behave “realistically” (within the rules of the world). Creating a visual and sound environment from this is actually not that difficult. This is almost all linear algebra and is a mature field of computer science.
The real trick is to do this process in real time. Over the years, game programmers have had to make many trade-offs between realism and performance (for example, if you can create a performance algorithm that will generate realistic trees that actually cost a lot of money). Thus, games over the years have become better (visually) as computing and graphics power have increased.
Now, some programmers have made real innovations in this area that (rightfully) earned them a lot of money. John Carmack (id Software: Doom and Quake) and Tim Sweeney (Unreal) spring to think.
The real value, however, in creating games is content. Just look at the credits for the modern FPS game (first-person shooter), and you usually see only 6 programmers, but there will be 30-50 + artists. Content is not complicated (from a software point of view). It will take a lot of time.
As for online games, I remember when Everquest came out and people raved about how much it was. Bzzzt, wrong. For those (like me) who were familiar with the development of MUDs (mutli-user dungeons) through the 90s (and possibly 80s), the Everquest server wasn’t so complicated in architecture.
The same goes for World of Warcraft or any of these games.
If you want to talk about a difficult state, what about the Windows XP operating system, does it all work, which estimates 40 million lines of code ? God knows how much Vista has. Or what about the Linux kernel?
Now in the government, in the military and private sectors, you will find other applications in which literally thousands of man-years are invested.