At first glance, the members of the Order of the Phoenix, the secret society that Albus Dumbledore founded, all seem to be good. Of course, since the Death Eaters represented the "evil" side, it seems fair enough for them to represent the "good."
And yes, while no member of the Order of the Phoenix revealed themselves to be evil (well, except Peter Pettigrew) some of them veered more to the "neutral" side of things.
Here are some of the members of the Order of the Phoenix and their probable Dungeons & Dragons Alignments.
Mr. Weasley- Chaotic Good
Mr. Weasley initially comes off as a very lawful guy, setting a good example for his kids to follow. Then we discover his passion for Muggle electronics and his flying car that he kept hidden from the Ministry, despite being a Ministry official himself.
Then when Voldemort returns, he secretly joins the Order of the Phoenix, risking his job and the safety of his family to do so. He even followed Dumbledore's orders and guarded the Department of Mysteries, even though he nearly died when Nagini attacked him.
Kingsley Shacklebolt- Lawful Good
Kingsley Shacklebolt is one of those interesting characters we never got to see much of. We know he worked with the Ministry, particularly with the Muggle Prime Minister and no one had negative words to say about him.
And although he came on behalf of the Ministry to arrest Dumbledore at Hogwarts, he was on the latter's side and was clever enough to not blow his own cover. And at the end of the books, it is Kingsley who becomes the new Minister of Magic, which sounds fair.
Mundungus Fletcher- True Neutral
Mundungus Fletcher always cared for himself. A sneak-thief and a pickpocket, he only cared about what would benefit himself the most. Although he wasn't evil by any means, he was often lax in his duties, such as the time he went off on his own chores and Harry was attacked by Dementors. He also stole things from Sirius' house when he wasn't looking.
And when he came face to face with Voldemort while escorting Harry from Privet Drive, he simply Disapparated, worried about his own life. Alastor Moody got hit with the Killing Curse meant for Mundungus, instead.
Alastor Moody- Chaotic Good
Alastor Moody had his own set of principles that he abided by, although he came off as quite unorthodox and paranoid. "Constant vigilance" was his motto. He was one of the best Aurors, responsible for the capture of many of the Death Eaters, and he was so suspicious of everything, that others often joked about it, even though they feared him.
He was also a good friend to Dumbledore, a thorough planner, and was dedicated to the cause right until he died.
Nymphadora Tonks- Neutral Good
Nymphadora Tonks was a Hufflepuff and one of the youngest members in the Order of the Phoenix. As a Metamorphagus, she could change her appearance at will. Although clumsy, she was nice and got along with everyone.
She even fell in love with Remus Lupin and did not care for the fact that he was a werewolf or his lack of wealth or the fact that he was way older than her. Even after she was pregnant with a child, she remained committed to the cause and returned to fight in the final Battle of Hogwarts where she ultimately died.
Sirius Black- Chaotic Good
Sirius Black was always reckless, doing things for his own amusement, although he never crossed over to the "dark" side. Along with James and Peter, he chose to break the laws and turn into Animangi, just so he could be with Remus in his werewolf form. He knew he was innocent and that truth helped him survive Azakaban for a long time until he broke out to take revenge on Peter.
He never had much faith in the law and had it not been for Harry's timely intervention, Black would have killed Peter in the Shrieking Shack itself. In fact, his love for Harry was so strong, he even rejected Dumbledore's advice and rushed to the Department of Mysteries to face the Death Eaters.
Remus Lupin- Neutral Good
Remus Lupin was always one of the "good" guys. He taught the students well, gave Harry sound advice, and joined the Order of the Phoenix to take down Voldemort. He also fell in love with Tonks and considered not marrying her, as he felt she deserved someone better. In fact, when Tonks was pregnant, he even considered abandoning her and joining the trio on their quest. But after confronting Harry, he realized the error of his ways and went back.
He also fought the Death Eaters in the final Battle of Hogwarts, alongside Tonks, and they both perished in that war.
Minerva McGonagall- Neutral Good
Minerva McGonagall, as the Deputy Headmistress of Hogwarts, was always strict and law-abiding. Although she cared for Gryffindor House very much, she did not hesitate to deduct points when they broke rules. Always keen to maintain law and order, she chose to resist evil, especially when Dolores Umbridge joined Hogwarts as a Defense Against Dark Arts teacher.
In fact, when Umbridge and the Ministry officials tried to sack Hagrid, she immediately came to his defense and took four stunning spells to the heart for her act of resistance.
Severus Snape- True Neutral
Snape's a pretty complex character and until his end in the last book, we weren't even sure of his loyalties.
Although it was finally revealed that he was Dumbledore's man through and through, Snape never had his own preference for good or evil. In fact, it may be argued that he initially was evil. After Lily's death, he chose to protect Harry not because it was the right thing to do, but because it was the only way in which he could atone for his guilt.
And that makes him a true neutral character.
Albus Dumbledore- Chaotic Good
Dumbledore was always on the good side. Very chaotically so, in fact.
He did not care if innocent people had to die, as long as they died for the right cause. Much of his later life was occupied with figuring out a way to defeat Voldemort and he manipulated people to put them at the right place at the right time, as that was the only way he could envision the Dark Lord's defeat.
In fact, Dumbledore knew that Harry would have to sacrifice himself and kept it a secret from him. He ensured that if Harry failed, there would be back up in the form of Ron and Hermione Granger to continue the fight in his absence.