1) The US government (or the World Security Council) wants either Clint or Bruce (could possibly be someone else or the whole team) to pay for something and sets out to arrest them. I think the team finds out while they're away on a mission in some other part of the world. The team decides to start helping and improving their public image in other countries where they cannot be deported back until the government decides to drop all charges against the person.
Found! by semebay The story is: What the Deep Heart Means
2) After a drunken bar fight in a back alley, Clint finds a stray cat who pretends to be injured. He brings the cat back to the tower. He starts out being drunk most of the time and feeling "sorry" for himself but throughout the story, he gets better because he has to take care of this cat. I don't think the cat ever gets a name. There is a sequel where Clint loses his sight(?) for a little while.
Found! by semebay The story starts at: This is a Story About a Cat
3) Through some magical something or other, Clint goes back in time and is able to basically redo all the events of the movie, making them "end" in a better way. He does tell Coulson, Fury and Natasha that he's from the future and they eventually believe him. I believe the beginning of the fic is him going back to seconds before Loki touches him with the spear and Clint throws up a mental shield that someone has been teaching him for if it ever happens again. Clint thinks this is a dream at first because he's been having this dream over and over again. This story is for sure a Clint/Coulson fic.
Found! by parmalokwen. The story is: A Chance Which Does Redeem All Sorrows The story is a WIP.
Now, these are only the ones I remember about/reminded about because of other stories that have similar scenes. There are probably a ton more that I'm missing. So, I was wondering if you guys have any recommendations. No mpreg and VERY-little-to-no Loki. I like Clint/Coulson, Steve/Tony, Steve/Bucky, OT6, gen or canon pairings. Other than that, anything goes. And I'd prefer them on fanfiction.net or AO3 because the program I use (Calibre) is only able to get fics off of those sites. Thanks in advance.