LOT'S of games that haven't been mentioned here, somewhat unsurprisingly.
Gary Grigsby's World at War, and its spin-offs, are probably the closest to what you're looking for, outside of Axis and Allies.
http://www.matrixgames.com/games/WorldAtWar/main.asp
In a similar playstyle, just with different scenarios, there's Gary Grigsby's War Between the States, a civil war themed game, and War in the East, which focuses on the Eastern Front of Europe in WWII.
Then there's slightly more complicated games, like
Making History: The Calm and the Storm, which is like Risk Plus, or Hearts of Iron Lite. Not too in-depth that it can be learned in a few hours.
http://store.steampowered.com/app/6250/
Moving up the "complication ladder", there's the AGEOD games. Very dated interface, and board game 'graphics', but as solid, in-depth turn based strategy as you'll find. These focus on specialized areas of history and geography, so little in the way of "world conquest" like Risk, but very good nonetheless.
Pride of Nations is one of the newest and most popular, focusing on the Victorian age.
If you enjoy that engine and gameplay style, there are several entries covering Napoleonic warfare, WWI, American Civil War, even the American Revolution
Also worth a look in the turn-based Grand (WWII) Strategy is
Strategic Command Pacific Theater, a very deep and intricate sim of WWII Pacific warfare.
Finally, and perhaps most recommended, are the various Paradox Interactive games. These are easily some of the deepest yet most enjoyable/accessible of any of the Grand Strategy games. Among the best are :
Europa Universalis III (IV is due to be released in just over a month)
Rome (NOT Total War)
Victoria 2
Sengoku (feudal Japan)
March of the Eagles (Napoleonic wars, almost exclusively combat oriented)
and finally,
Hearts of Iron.
Quite simply, there's nothing better at what it does. No strategy game is a deep, intricate, or does all that it does as well as it does it, like the Hearts of Iron games. Period.
Be warned though, they are quite complex. This is nothing like Civ or Total War. Watching a few Let's Plays on Youtube is probably essential for getting the hang of it.
I highly recommend Hearts of Iron III, with the latest patches and expansions. Darkest Hour, a Hearts of Iron 2 expansion/spiff-off is excellent as well and slightly more user friendly, but learning HoI3 with it's intricacy and versatility still makes it the better game overall.