...Still, the genre is filled with non-heroic heroes. Fafhrd and the Grey Mouser were unrepentent thieves, and occasional hit men. Conan stole everything he couldn't have sex with or kill, and a few things he did. Elric of Melnibone was never a nice man (even if his enemies were worse), and had no problem devouring the souls of people to 'power up.'
There's the occasional Three Hearts & Three Lions type character as well, but they aren't exactly the norm.
Our modern media goes a step further, with movies that celebrate ultra-violent assassin characters (Wanted, Pulp Fiction, The Replacement Killers, Kill Bill, Pitch Black/Chronicles of Riddick, even James Bond, to an extent) or cops / agents / lawmen / soldiers who take the law into their own hands to 'get the job done' (John McClaine, Jack Bauer, half of John Wayne or Clint Eastwoods characters) or even primarily 'good-guys' who come from morally gray backgrounds (Seely Booth from Bones, former sniper, Ziva David from NICIS, *hawt* Mossad assassin, Wolverine, psychotic manimal dwarf ex-assassin/samurai/lumberjack, etc.)...
Note that this is *not* a 'things were so much better in some mythical golden age, society is declining!' hand-wringing. Heroes of myth and legend (and even the gods) behaved terribly, sometimes striking people dead for even looking at them funny. We've pretty much always glorified people who take what they want and scoff at restrictions that we have to follow, whether they were named Hercules, Conan or Riddick...