The First Law trilogy
First Law by Joe Abercrombie. It's witty, intelligently plotted, the characters are all grey, and there's a ton of brutal action in the books. Abercrombie writes some of the best fight scenes in the genre, and his portrayal of war and battle is spot on (especially in his later books like The Heroes) and will make you really think about the ultimate cost of war. One of the best series that's come out in a few years -- one that actually tries to do something new in the genre. Even better, with every new book added to the series (or universe), Abercrombie gets better and better. It's similar to Martin's work in the sense that there is really a moral compass -- good and evil are just both sides of the same coin. Heroes are not made out to be noble paragons: they are just straight out meaner, stronger or more conniving than the rest.
Prince of Thorns
If you like the grittiness of Martin where the boundary between heroes and villains is thin, Mark Lawrence's Prince of Thorns is an interesting take on the Anti Hero. This is the singular tale of a hero on a quest for revenge and glory (which eventually involves saving the whole world) but the flawed humanity present in Prince of Thorns channel the shades of Martin's brutal take on a fallen and immoral knighthood.
Acacia
Try David Anthony Durham's Acacia . It's has a somewhat similar feel to A Song of Ice and Fire. The series wasn't as good as it initially promised to be by the end of it, but it's still good enough to read; the author pulls some interesting plot threads out of the blue by the end of book 2. My major complaint about the series was that I never really found the characters all that interesting.
Elric
Elric of Melnibone by Michael Moorcock. Elements are similar. You have incest, kingdoms on the cusp of decline and ruin, pacts made with monstrous powers. The landscape is dour and the heroes are partly villains.
The Godless Word Trilogy
Another series that had a somewhat similar feeling to Martin's work is The Godless World trilogy -- there are some shared elements between the works or at least the gritty, dirty feel of A Song of Ice and Fire is shared by both works. The Godless World is actually more like a cross between Martin and Tolkien's Lord of the Rings. I did find the quality of the series dipped by the end of the trilogy, but it's still a good enough read.
The Dagger and the Coin
Daniel Abraham's The Dagger and the Coin series. Rich characterization with characters you dislike who eventual grow on you as the story progresses; oh my god -- plot twists and turns, and magic that's not at all present until the story progresses. Not as much action and drama, but a more character driven saga.
Sword of Shadows Saga
Sword of Shadows is pretty close to Martin in terms of the setting and the portrayal of gruesomeness. The setting is a cold, brutal, Arctic-ice world. It's not as "grand" or "epic" as Martin and the cast of characters is not as morally ambiguous. Still a pretty damn good read, though the author is taking her sweet time finishing the damn series already.
The Black Company
I would be doing you a disservice if I did not recommend Glenn Cook's The Black Company series. It's gritty military fiction with a cast of grey characters, and great battle scenes -- something that Martin focuses on in his books. The focus of the series centers on a company of soldiers.
The Farseer Trilogy
If you like reading about Jon Snow, you might give The Farseer trilogy a read. There are some shared story elements (though the plot and world is NOTHING at all alike mind you). Farseer is pretty much the story of a young king's bastard who grows up in a castle full of intrigue. He doesn't have a lot of options and struggles to survive, and in the process gets tangled up in a series of political schemes. The main character also has a special relationship with wolves (he can speak to them mind-to-mind via a magical skill called the 'Wit') so you might read this one if you like the whole Stark and Direwolf thing. Some of the best characterization in the fantasy genre. Be warned: Jon Snow is a lot more bad-ass of a hero though.
Malazan Book of the Fallen
Steven Erikson's Malazan Book of the Fallen is a must-read, and it's a finished 10 books long. There are some elements that are similar to Martin's work: it's got gritty and intense battle scenes, a cast of ambiguously grey characters, main character deaths, plenty of brutality that characters inflict on each other, and unpredictable (and utterly massive) plots. It's quite similar to Martin in the way that the line between villain and hero is quite blurred. You often end up rooting for characters on both sides of the war. No one is really "the hero" and every character is either trying to maintain their power status quo, or steal it from someone else. However, the work, as a whole, is a LOT MORE disjointed than Martin's work (even counting for the fact that Martin has lost his way a bit)
The Darkness That Comes Before
Try R. Scott Bakker's The Darkness That Comes Before, which features superlative prose, a unique, but fascinating storyline, and the gritty realism that Martin exhibits. It's got that world is ending element to it as well. It's also a heck of a lot more philosophical too, which may or may not be something you like. On a whole Bakker's work is sort of like Tolkien's Mordor invades Martin' Kingdoms and stirs up a lot of shit. Throw a fantasy wizard Jesus with kung fu abilities and stuff the prose subtext full of philosophy. On the surface it's a head-case trippy mix, but there is a certain power to this series.
The Grim Company
The Grim Company by Luke Scull. There are elements of Martin in this work, which I was very impressed with as debut novels go. It's very much so a dark fantasy, with brutal violence, death, magic, and some compelling characters who are all flawed. You'll feel right at home if you are a Martin lover.
Monarchies of God
Monarchies of God -- a vastly under-appreciated series. If you like the epic struggle between kingdoms, fierce battles, strange unexplored lands across the sea, and life aboard a ship. Paul Kearny writes a compelling tale here. Elements of grim dark too.
Shadowmarch
You might also like Tad Williams newest fantasy saga: Shadowmarch which has some similar plot elements (strange fey creatures coming down from the north behind a wall of magic mist, trying to take over the world). There's a rich cast of characters scattered across the world in completely different lands (much in the way that Martin features characters living in the frozen north, characters living in exotic deserts, and so on). The creatures the north, the Quar, are similar to the Others, but more developed as mysterious, yet somewhat sympathetic entities, rather than the zombie-making horrors that Martin makes the Others to be. You might say this is the story of "The Others" and how they came to be so damn pissed off at the world of men.
A Land Fit for Heroes Trilogy
The Steel Remains by Richard Morgan, of Science Fiction fame. Marin can write villains as heroes and heroes as villains, but if you want to read about a dour world without a shred of goodness, check out Morgan's foray into the fantasyscape. Its a dark and blood and cold as ice, but there's a shit load of brutal action.
Coming of Conan the Cimmerian
Because...like Martin himself recommends Howard's masterpiece. What more could you say to that?
Lies of Locke Lamora
The Lies of Locke Lamora by Scott Lynch. Elements of ASoIaF's gritty and dark but at times hilarious. Well written. Think a book made up of the Tyrion chapters, centering around a band of thieving scoundrels in an Ocean 11 fantasy plot.
The Amber Chronicles
The Amber Chronicles by David Zelazny. Take a royal family who can walk into different realities. Gray characters, squabbling siblings, alternate realities, a prince in exile.
The Gap Cycle
The Gap Cycle by Donaldson. This is science fiction NOT fantasy and in no way is there any similar plot elements or themes, but Gap Cycle is darker than dark and features heroes who have more in common with villains. If you like the bleak outlook on flawed humanity taken up by Martin, Gap Cycle won't disappoint your disappointment in the human race.