Jed I. Knight
The Mos Eisley Hillbilly
Abercrombie is arguably the closest author to Martin. His books are even darker and the line between good and evil is completely in-existent (in Martin's books, it is very thin), while at the same time his books have the best humor in fantasy genre. World building is decent, while characters are excellent, although a bit repetitive (basically, all are pricks of the highest order).
So, far he has two sagas. The First Law trilogy which then continues with three standalones set in the same world and which share many characters with the trilogy. And The Shattered Sea trilogy which is a bit more juvenile, but still it is very Abercrombie-style. The Shattered Sea has a better writing and it is significantly shorter, but The First Law is better. In fact, it is easily one of the best things in the fantasy genre.
What Revan said basically. If you like Martin you will probably like Abercrombie. He's my favourite author by a distance at this point and I'd recommend him to anyone. Start with The First Law trilogy.
Brent Weeks Night Angel trilogy is pretty good too, but might be a bit of a departure from the authors you mentioned.
Just dropping in to mention that I finished The First Law trilogy a while back, and wanted to thank you again for the suggestion. It was a very good read, indeed. If there was one thing I found a bit lacking, it was character development, but that again of course fits in entirely with the overall theme of the series. Not really sure yet if that, ending included, was brilliant or just annoying
Anyways, I'm going to read the standalone books next, I reckon. Haven't delved into them at all, so excited to see what they are about. The mythology was probably my favourite part of First Law, so I'm really hoping one of them dives deeper into the backstory.