It's hard to describe her as fan character, but that's a character that I like because for both canon and fanon things. I'm talking about Rin Satsuki.
So now, why do I like her so much ? Because I like the idea of a "good youkai". Of course, there are some helpful youkai in Gensokyo, but I wouldn't put them into the "sacred" category.(that part is mostly present in fanon works) She's a nurse and posses wind and flower power as well as playing a musical instrument. I would have been cool to have a recuring character who attacks with the help of music.
She's oftenly decipted as kind and cheerful, which I like a lot and contrast with the "bored" personnality of Reimu and "crazy" personnality of Marisa.(even though the two of them are different in 98)
Now there's something else that makes me like her, it's of course her situation of an "unused" and "forgotten" character. While she's considered as a cheerful and sacred character, she's also decipted as a "tragic youkai who could never exist", and honnestly, that's something I find very sad. She's . . . kind of existant because of the fanbase and will also stay unexistand, because she's semi canon, and her canon part consists only of some information about her . . . and that's something that will never change.
That's also an interesting thing in her, she's both fanon and canon. She's both lively and somewhat "dead". She's really interesting and touching.
I think that "Dreamy Pilot" that JynX gave her as a theme really suits her, an unused and sad song for an unused character.