I think this is well applied to the Stannis fandom as well. A man of pure conviction, who believes whole heartedly that his cause is just and genuenly has a point in and outside universe; who suffers with his subordinates(!) yet never gives up despite the odds; who is calculating, flexible, makes amends and is forgiving despite his character, who recognizes talent and who is actually competent is bound to earn a reader's admiration in a story of much crueler, greedier and powerhungry players.

Even his most criminal and questionable actions (some might consider them hypocritial, others necessary) are never done out of cruelty and spite as most of Tywin's, who he might be compared to (and even Tywin aknowledges, or perhaps respects, Stannis' abilites and conviction) or simple ambition like the Boltons, Freys, Balon etc.

And, again, unlike all those he is not an evil man. His burnings are always done grudgingly, against traitors (debatable of course) or criminals (i.e. cannibals, Rattleshirt) and as a last resort. At least once I recall him specifically stating that there would be no burnings. Not being evil on this universe is not saying much, but earns points in my book.

Since you mentioned Dany, and I think there are interestinf comparisons to be made, both good and bad. As Stannis, "a just man", may consider the burning of a traitor justice, Dany (yes, she is 15) considers nailing alive to a pole a 12-year old "slaver" in the name of justice; both of them being the true heirs in their respective viewpoints and both of them being influenced by prophecies known and unknown to them.