Some people are extremely bothered by trivial justifications (myself included!). If the guy slaughters a dozen enemy soldiers without wincing, then cries when he has to put a deer out of it's misery "because it was humane", I want to vomit. I think Limrael (?) or one of the writers who has a long list of rant/suggestion/something posted something like this. She also wrote something along the lines of "likeable bastard". It's all good stuff - should be a link somewhere in a stickied post.
Then again, that would be inconsistent too. Except, if the character at one point reaches a breaking point - but that would have to be preceeded by sufficient hints as to the approach of this point, it would be very hard to win the reader's sympathy on this. But, sure, many books are featured by a 'bad-ass', the cold killer knowing no mercy nor sentiment. Readers often do fall for that. If you can slay a dozen men and not wince, doesn't it make you admirable in some way? The reader thinks so, except perhaps when this main character goes all sadistic and homicidal.
I know tons of people have already replied to this, but I had to mention Macbeth. In the famous tragedy, Macbeth is a murderer, and yet he is still considered a "tragic hero".
Hey Thomas Covenant rocks!! but no seriously... although that bit was slightly edgy the rest was allright... and Covenant never set out to be a hero in the first place! that was his charm, that he was totaly unhero-ish and kept making mistakes he couldn't live with. the predecessor of the modern emo. i know this is totaly off topic but i just couldn't not defend Covenant. And so back to the original question. i think no one is beyond redemption. even the most evil of villains can still get up at the last minute and take a bullet to right their wrongs... and i personaly think the wickeder the main character is the more people like him. as long as you can explain why they act the way they act, people tend to feel sorry for them for falling into their unavoidable predicament (spelling??). no one is interested in a goody two shoes... PS woops as soon as i see someone badmouthing Covenant i have to say something. only now do i realise someone's already made my point...