Title speaks for itself. Take a DC hero, villain, supporting character or even a civilian and put them in a group or team that they have never been a part of.
Dick Grayson- Suicide Squad: Ever since Grayson and seeing Gunn's Suicide Squad, I always wondered how Dick would fit in on the Squad and how he would lead a group of villains as opposed to a group of heroes. Would he get along with them? How many lines would he allow them to cross? How will he keep them in line? Would he be forced to resort to Waller like tactics as well?
Green Arrow - Challengers of the Unknown: Ollie has managed to inexplicably survive dangerous situations with just his bow and arrow. He would be a great fit for the team and as well as being the new guy and a known hot headed disrupter he would force other Challengers to react to him.
Atom/Ray Palmer - Justice League Dark: Ray's a scientist but his book was once briefly a sword and sorcery book and he has an underrated friendship with Zatanna. Moreso than Man-bat I think Ray is a much better fit for being the team's resident scientist.
Wonder Woman - Legion of Superheroes: The LOSH is largely centered on Superman but it is the one major superhero team of the DCU set in the future. It's weird that we don't see any impact WW could have had in the future. Plus Diana at her heart is an adventurer so an adventure set in the future seems right for her.
Donna Troy - Seven Soldiers: I was thinking of a non-Titans team that she could be a part of. I'm thinking that this is a team that's a mix of different rosters and modern versions of old members like Roy Harper, Frankestein, Shining Knight, Crimson Avenger, Wing, Star Spangled Kid, STRIPE and Manhattan Guardian.
Vixen - Justice League Dark: Vixen not being a part of the JLD is weird. She is magic and connected to West African mythology through Anansi. Think of the possible interactions between her and Swamp Thing who commands the Green. Plus she has some history with Zatanna and Wonder Woman as well.
Zatanna - Justice League International: I'm itching to see Zatanna in a light hearted setting. I love the Giffen/DeMattis run and think of the hilarity that Zee could bring to the team like turning Guy into a rabbit or the trouble she could get into with fellow showman Booster Gold or maybe Booster and Beetle managing to talk her into taking part in some kind of scheme that blows up in their face. The possibilities are endless.
Black Canary - Infinity Inc: Even though she is a JSA legacy hero, I don't think we've ever seen BC on the team made up of JSA kids. This could lead to some interesting interactions between her, Jade, Obsidian, Hector, Courtney and the other JSA kids.
Jimmy Olsen - Newsboy Legion: I don't think this has been done before but he would be a perfect fit.
Or if you want him on a team that he's ill suited for:
Jimmy Olsen on the Suicide Squad: Interpid photographer gets into more trouble than he is worth when he goes on a overseas assignment where he has to work with the Squad to save his life.
Amanda Waller - Teen Titans/Young Justice: We all know how Amanda Waller would handle things if she was put in charge of a group of bloodthirsty murders whom she has to cajole and manipulate into doing some good but what happens if you put her in charge of a group of young, impressionable, children with superpowers whom she has to assign missions to?
Fire & Ice - Birds of Prey: Given the international nature of the team I always thought these two would be a good fit. Thinking of pre-Nu52 BOP here.