There are some unaffiliated characters that are natural fits in certain affiliations: Shuri in Cabal, Loki in Avengers, Thor in… pretty much everywhere. But here is one character for each affiliation that I’m not seeing played much, but I think should be being considered more.

Avengers – Killmonger
Killmonger fits really nicely in to Avengers. Not only can he charge for one power less, but he has a great protection mechanism in Cap’s bodyguard. Avengers can often play the long game and can favour slower scoring crises that allow them to take advantage of more powerful injured sides of Cap and Iron Man, get more value out of their leadership ability and plays to the strengths of Second Wind, whilst being kept in the scenario game by Avengers Assemble. In those situations, having the option to jump ahead two with Usurp the Throne can make a real difference.
Cabal – Rocket Racoon
The Cabal have long suffered from lack of a good two threat option. Black Widow is a decent objective runner, but doesn’t always make the most of the leadership ability and if she does doesn’t have good ways to spend the extra power. Rocket, however, revels in having plenty of power to unleash massive shots from way downtown.
Wakanda – Doctor Octopus
I’ve written about my Wakandan list a few times, but I’m calling out Doc Ock specifically here. He plays in to the push/pull archetype, which whilst not the only way you can play Wakanda, is a very effective strategy on some crises. He’s a second 3 threat thrower after Valkyrie, who is also a great Wakandan. Unlike a lot of characters, Ock can find himself with more power than he knows what to do with, so having the ability to spend power on rerolls is a great use of his power, going fishing for those excellent wild effects on his attacks, or replenishing the power whilst getting an extra success by getting a Critical. Everybody loves getting Vibranium Shielding, but Ock has that chunky 4 physical defense to help make him even more durable.
Asgard – Iron Man
Iron Man has two things going for him in Asgard: he’s a cheaper character in an expensive affiliation and he’s really quite hard to damage. The Asgardian built in healing is much more valuable to characters that are hard to damage in the first place. The way the maths falls around Invincible Iron Man, he often takes one damage (~40% of the time across a good range of attacks), and therefore generates one power. Out of his activation, he can just spend that power to reset that attack, leading to wasted activations. And that’s ignoring all the times he takes no damage.
Any future characters with a similar damage reducing mechanism will benefit equally much from this.
Guardians of the Galaxy – Ultron
I’ve had quite a low opinion of Ultron for a while now. Except maybe when he is dropping off Venom, for me, he needs his Age of Ultron tactics card to really merit inclusion in a roster. The trouble is that is too easy for your opponent to play around – ignore Ultron, or push him away so he becomes less relevant and never even try to KO him. Alternatively, judicious use of stun can stop him building up the power he needs. Guardians fixes that problem: Age of Ultron can be cashed in at any time for Winging It. It allows you to go hard with Ultron early, setting the line on battle high, and possibly also dropping off another ranged blaster style character.