In Role-Playing games, there is a thing called Character Alignment (or simply Alignment). It is basically a table of "Lawful, neutral and chaotic" values versus "good, neutral and evil" values. I think it is a good way to "classify" fantasy characters in general. Here's a picture by Artist_Incarnate  that shows some examples:
Personally, I think we agree that Stannis Baratheon is a lawful person. I mean, we know that he is seeking to be king because he really is the next on the succession line. However, he is certainly not a totally kind or bad person. I think he is rather neutral, because I can't remember a time when he decided anything for himself and not for the good of the Realm.
Answer by Nicholas Saint,
There are plenty of much nastier characters out there, but Stannis is definitely a bad guy. And he's bad in a tragic way, because he is a failure of a person according to his own worldview, though he refuses to see it.
Stannis is living his life fueled by outrage over the injustices done to him. He treats the laws of inheritance and succession as sacred and utterly condemns those who violate them. For years, he was consumed with bitterness over Robert's decision to give Storm's End to Renly, so as to have the more imposing Stannis installed at Dragonstone. As the second oldest brother, when Robert took the crown, Storm's End should have passed to him. Those are the rules, and Robert took what was rightfully his. To Stannis, Robert's strategical considerations were irrelevant.
In the wake of Robert's death, Stannis knew he was the rightful heir, and he could not understand why that wasn't the only thing that mattered. And his rage over what should be prevented him from seriously engaging with the world as it actually was. When the Starks offered him a treaty, wherein they would recognize his claim to the Iron Throne if he would accept the North's secession, he rejected it, not because he didn't think it strategically wise, or because he particularly *wanted* the North, but because he simply refused to negotiate for something he felt was already his.
Over the years, he has also developed an extreme ends-justify-the-means morality, at least as it applies to him and his quest for the throne. If burning non-believers, killing babies, or destroying churches will help Melissandre help him, then those things should happen.
All of this is fueled by that simple understanding that the rules say he is the next king, so nothing else matters. If someone else is more popular with the people, or better at this or that, it is irrelevant. If some other outcome would result in less bloodshed, it is irrelevant. It is rightfully his, and that's all there is to say.
The crown is rightfully his because Robert, aided by Stannis himself, rose up and killed the rightful king and installed himself on the throne. Stannis is only the rightful king if Robert was as well, and Robert is king not as a result of these sacred rules, but because Aerys was such a nasty piece of work everyone was willing to press the reset button.
He knows this, and it fills him with rage and self-loathing, but he nevertheless sticks to his self-righteous bloody crusade.More questions on Game of Thrones (TV series):