The thing with an antihero that does heroic things but not for other people's sake, is that he's a bit empty. Selfish is usually all you need to describe such a person, since he's only out to get the uber sword from the dragon, and doesn't really want much more. It's an 'I want, I take'-approach, which makes a character pretty cool (usually, people are sick of goody-goody characters), but hardly fit for a main character, unless they change over the course of the story.

It gets more interesting when a person who does heroic things for himself comes across a person who does less heroic (or even abominable) things, but because it's the lesser of two evils.

Actions are considered good or evil according to moral

A anti-hero/evil-hero/good-hero is formed not by his actions but by
his reasoning why.

One has to be carefull there is a fine line between a more evil hero, a good hero and a anti-hero. A evil or good hero does things due to his moral code and set reasoning point, a anti hero is mostly thrust in the middle of where a good or evil hero normally wants to be and is needed and will act in response to the situation and more or less self preservation he/she does not want to be a hero but has to fill the gap for better or worse at least for themselves or another reason.

A Good or evil hero may quest to slay a good or evil dragon, a anti hero might find a dragon attacking him and no where to run. Both succeed in slaying the dragon, both are hero's but both for different reasons. For the good or evil hero the reason was mainly dictated by his/her moral view and secondairy exterior motives, for the anti-hero it is dictated mainly by exterior motives (the dragon attacking) and less by moral reasoning.

(Kill the king or your wife dies :
a good hero will try to safe both and undo the villain,
a anti-hero will kill the king or try rescueing his wife but if the villain does not chase the anti hero he may be left alone,
a evil hero will let his wife die and kill the one who threatend him/her and then get that crown for him/her self)