Instrumentalities of the Night
If you like Black Company, you should definitely read his other fantasy series, The Instrumentalities of the Night. It combines an ancient evil coming-back-into-the-world plot, a military genius hero, plenty of conflicts between worldly powers, political scheming, all filtered through Cook's military narrative. The closest you'll find to The Black Company in style and form. And duh, it's by the same freaking author. How much closer CAN you get?
Starts with Scourge of the Betrayers. About as close as you are going to get to Cook -- the narrator is even an archivist and the tale is told in first person. There's a LOT of similarities and the Bloodsounder books are gritty gritty grimdark dark. Delicious and some of the best fantasy to come out the past couple years. Do NOT pass this series by if you want something similar to The Black Company. It's the best of the similar recommendations I can give.
Malazan Book of the Fallen
For another "dark" military fantasy, you should read Malazan Book of the Fallen. It's more epic in scope than The Black Company, but there are enough similarities that you'll find yourself right at home. Steven Erikson has even stated that Glen Cook's books were an influence on his own writing, so there you have it.
The Dagger and the Coin
You may want to give Daniel Abraham's The Dagger and the Coin series a good go at it. Books one and two are out and they are seriously good -- some of the best epic fantasy that's come out. Abraham's work is a good mix of epic and military fantasy with some smart writing and a cast of compelling characters (some which are anti-heroes). Both are character driven, though Black Company has a hell of a lot more action and angst while The Dagger and the Coin is far more about the characters. It can be somewhat plodding and slow at times. However, if you like Black Company, and military fantasy with strong characters, you may just like this series.
The Ten Thousand
Paul Kearney's The Ten Thousand is a superb military fantasy by a much underrated author. If you like Black Company, you'll dig this one hard.
The Way of Kings
Sanderson's awesome The Way of Kings is also another book you might want to read (it's first in the Stormlight Archive series). The main character (Kaladin) has a few basic similarities to The Black Company main character (Croaker). Both are retired physicians who've given up their profession to become soldiers. Both lead a squad of men (and there is the squad dynamics). Cook's work is more gray and his style more dry, however. The narrator (Croaker), is not a crazy badass super hero, while Sanderson's work is more heroic in nature as is the character. So don't get the idea that The Way of Kings is anything like The Black Company as a whole, but as stated there are some similarities.
Heroes Die by Mathew Woodring Stoover. Dark and gritty world. Check. An anti-hero character who ends up working for the bad guys most of the time? Check. Explosive and brutal action? Check. Strong characterization. Check and Check. Heroes die is MORE about a singular hero than a company of characters, as is The Black Company, but there's enough that you'll probably love it if you like Glenn Cook's work.
The Darkness That Comes Before
The Darkness that Comes Before. Ah, grimdark epic fantasy at it's best, but not your standard epic fantasy: this shit is deep and philosophical. Lots of wars and grand military battles and dark gods taking over the world. There's nothing else quite like it to be honest, but ignoring all the philosophy sprinkled between the chapters, there's a hell of a lot of bloody action, gratuitous sex, character development, and political intrigue to keep you turning the pages. Oh and there's a world-ending apocalypse coming.
The Coldfire Trilogy
Black Sun Rising is a different sort of work. But it's a very dark and grim world featuring an anti-hero character and side kick heroes that are all flawed individuals. One of the best fantasy books in the genre. You'll probably like it, even if it's about a couple characters solving a quest rather than a military band caught up in incessant warfare.
The Thousand Names
The Thousand Names by Django Wexler. This is a new series that came out in 2013 with two books out so far (the last one was out a few months ago, mid 2014). If you like large scale battles and the story of a squad/company facing extreme survival odds in a foreign country, you'll love this series. It's one of the better fantasy books to come out the past few years. And it's certainly one of the best military fantasy series since Erikson's Mazalan. If you like Black Company, you'll love this series.
Legend by David Gemmell. A classic, but one all about a hero fighting an endless war against endless odds. There's something of beauty in this heroic treatment of an old washed up hero who's pressured by the need of his people to come back from retirement to kick some ass.
The Red Knight
For a very medieval fantasy with magic and monsters and knights, Miles Cameron's The Red Knight. This was one of my favorite reads of 2013. There's a lot of military battles and squad/company warfare against foes with superior numbers. It's not as dark, on a whole, as The Black Company, but it's a stellar read. If you like might and magic and battles and warfare, this is one for your.