1. They interact in canon, preferably in a significant (apply your own interpretation of such) way.
2. They are not related. They can, however, view each other as surrogate family.
3. Neither has confessed or implied romantic love for the other in canon.
4. They have not dated, been married, had sex, or made out in canon, on purpose, and of their own free will.
5. A popular fanon ship is ok (though preferably not your ship) but a canon pairing you wish were just friends is out.
6. Try to avoid using the same character or series twice.1) Barbara and the First Doctor in Doctor Who. Barbara is the reason the Doctor is the man we know. She made him a better person – by being determined and compassionate and brave and not taking his crap. He kidnapped and scared the hell out of her, but also showed her the universe, put her in positions she'd never have been in, made her grow into someone even more magnificent.
Also, she reminds him of his wife. 2) Tobias and Cassie in Animorphs. If Rachel is his connection to human interaction, Cassie is his connection to human compassion. She's so very strong, and so very kind; the combination assures him, and inspires him. Tobias, in turn, reminds Cassie that predators are predators, and she can accept that. She understands him in ways others don't, and he her.
3) Remus and Harry in Harry Potter. I really wish we'd got more of them, after Prisoner of Azkaban. Remus was someone who cared about Harry for himself, not his destiny, who became a solid, comforting presence, who taught him valuable lessons in and out of the classroom – deliberately and not. Harry reminded Remus of his parents, yes, but he was also someone else entirely – someone Remus could love again. I think Harry was the first person in decades he allowed himself to become truly close to.
4) Wesley and Gunn in Angel. Two very different people, united in a common cause and bonding as they fight side by side. There are issues, of course – foremost Wesley having to be a leader first and a friend second – but that just makes it better. It's spoiled in season three by the tedious love triangle, but it was awesome while it lasted.
5) Tara and Dawn in BtVS. They both lingered on the outskirts of the Scoobies; Willow's girlfriend, Buffy's sister. Tara took Dawn under her wing, assured and comforted her, made an effort to understand. When Buffy died, it was she and Willow who became her guardians. I think Tara became the most important person in Dawn's life after Buffy.
6) Xavier and Jean in X-Men. "I like to think Jean knew. Knew, and understood."
7) Sookie and Terry from the Sookie Stackhouse novels. Terry is a minor character but a resonant one, and his quiet fondness is sweet. They accept each other, something they both need more of.
8) Future Gohan and Trunks in Dragon Ball Z. 9) Geordi and Data in Star Trek TNG.10) Eric and Sarah in The Crow.Excluded: Tobias and Ax as they're technically related, Cordy and Angel because season three sucks they end up falling in love, Remus and Sirius since I can go either way, Remus and Peter since it's mostly in my head, Angel and Kate because I do think they started to fall for each other. (Really, Angel and a lot of people. Wesley had a major crush, Spike so shagged him at least once, etc.) Nico and Karolina as the latter has a possibly unrequited crush, Sookie and Sam as they're very definitely attracted to each other, Ed and Winry as I hear it gets romantic, NCIS because I ship everyone...I shall now resist the urge to do an entirely Doctor Who version.