Our shiny wiki says, in the FAQ: For Other People, that a good OC exists to serve the story. A Mary Sue exists for the story to serve her.

My idea of a good OC is sort of a combination of what Tungsten_Monk and Phobos said. An OC should fill a gap in the world - a role that conceivably exists within the canon's guidelines, that hasn't been filled by a canon character. A continuum like Doctor Who, say, is very conducive to OC protagonists, because the Doctor is always hopping around the universe meeting new people; a continuum like, I don't know, Homestuck is very non-conducive to OCs, because there are a very specific number of people who are even capable of being alive during the story and we have been very well introduced to all of them. (Admittedly, I am a canon purist; if it contradicts canon at all, I'm generally predisposed to dislike it. I always prefer the "plausible deniability"-type stories - it could have happened in canon, we just didn't hear about it.)

On the other hand, even if the OC blends seamlessly in with the world, if s/he is flat, unconvincing, and canon-warping as a person, s/he's still not a good OC. Being a plausible, well-rounded, three-dimensional character, with actual depth, with a history, with hopes and fears and strengths and weaknesses and goals and her/his own and legitimate reason for existing, is the most important consideration when writing a character, whether in fanfiction or original fiction. Being beautiful and powerful can be part of that description, but there must be a believable reason for it.

TL;DR - Agreeing that the most important thing for a character of any stripe is depth. Fanfiction just has the extra challenge of having to fit in with an already-established world.

A Good OC explores the canon and its world.

Every character in canon shows us something about the world. They teach us new things. In a way, they are how we experience the story and the world it takes place in.

A good OC follows this lead. With that character, we can come along and explore the world. And their perspective and presence shows us something no other character could have shown us.

This is why bad OCs spend so much time making us look at them. They draw attention from the other characters and plot to basically shake their rumps in our faces. They don't take you by the hand and show you anything, much less anything meaningful.

This is why Agents as good OCs is crucial. We come along with them on the mission, they show us the story. If they spent all their time forcing us to stare at something rather than taking us on an adventure, then they'd be bad at their jobs.

I pretty much agree with everyone so far. All of these things are necessary in fanfic: sharing the spotlight with the canon characters, adding something, being a good character in general.

To me, it adds up to plausibility and impact. I have to believe that character could be there as they are and do what they do, and get away with it in a canonical context. If the people around the OC don't react in a way that makes sense for them, then I can't believe in the OC.

There's obviously some leeway here, since no one who isn't the author of a canon can write those characters in exactly the same way, and the presence of an OC in and of itself may give them cause to react differently (in an AU, say), but it all still has to make sense generally, if not in the specifics of word choice or writing style. The OC shouldn't by its presence alone contradict known canon—or if it does, the change(s) need to bloody well be explained, preferably as part of the story. "Snape has a daughter in this story, k?" is not an explanation, but "What would happen if Snape slept with someone after Lily died and had a child?" could make for an interesting story. It would probably have to be about Snape in order to work... once it's about the OC, the potential for problems increases. Not that it couldn't be from the OC's point of view, though. The POV character isn't necessarily the one the story is about.

... I am now rambling. Guess that's enough of that. TL;DR, anything can be done well, but an OC's existence has to be plausible and have an impact that makes sense.

~Neshomeh

Either a character that needs to be there to help to best tell a story revolving around the main characters, or who, when the central character, is not showcasing their own awesomeness but reacting to events in whatever time and place their story is set in a relatable, realistic way.

In other words, one who serves the plot well to tell an interesting story.

I think that the key to making a good OC is to make a good character. For a good character, you need to answer four questions (bonus points if you know where I stole these questions from.) They are:

Who are you? (Everything from name and age to sexual orientation, religion, and general outlook on life)

What do you want? (Do you want to avenge your father? Make some money? Live in peace? This should be easy. What do you want right now)

Why are you here? (How did you get where you are emotionally, physically, intellectually, spiritually, et ceterally?)

Where are you going? (Long term goals and dreams. As long term as the character is likely to think.)

These four questions do not guarantee a good character, but they do help you along the way. It is not a bad idea to answer these questions with every character you have. Specific detail isn't important; I don't need to know when you character lost their first tooth, unless it is important to the story. Also, everything you come up with for answers doesn't need to make it into the story, but it will fuel the story through your characters' choices.

Please note that the answers to these questions can and should change through the course of a story. What you want can change very quickly, the others take more time, usually.

I have have a post that I moved to my new blog that talks about the concept of the protagonist, which doesn't talk about this concept, but talks about things that are necessary, above and beyond the questions, to make a good lead character.

-Phobos, who is testing a lesson plan on the Board

To me, the ultimate consideration when writing an OC (in a fanfic, anyway) has been whether or not this character specifically adds--in a positive way--to the universe, rather than changing or removing something that has already been established about it.

That's a little obtuse, so let me give you an example. I'm currently writing GI Joe fanfiction (I know, I know--mock away), and one of my stories does indeed center on an original character. I wanted to use her to get a unique perspective on the rest of the Joe team. I could create a new special branch of GI Joe, headed by my character . . . Or I could fit her into a role that the canon universe implies but never defines, that of quartermaster and base cook. A role that already exists, but was never filled. No canon characters or circumstances need to be specifically altered for her to exist, she adds the perspective of the cook and perpetual onlooker, and everything works.