A lot from his relationship with Mockingbird, especially when in the hands of Jim McCann. Most notably was her finally conceeding to the fact that, no matter where she goes, Clint will always be there to help her, be it fighting some villains, doing spy work, or merely being here when she needs someone.
In the new series, there's about one every issue between Clint and Kate. When there isn't, instead there's one with his apartment tenants, or on occasion someone else:
Issue 1: Seeing that they're going to be kicked out otherwise, he buys the apartment building and lets them keep living there for low rent, since he doesn't need their money.
Also in Issue 1: Him paying an operation for a dog that's not even his because the jerkass tracksuit gangsters seriously injure him.
Issue 2: Him getting terrified when he thinks she might have died, or been seriously injured, by the new Swordsman and his gang.
Issue 3: Her saving him with his boomerang Trick Arrow, after previously making fun of it.
Issue 4: Her following him even though he told her not to, and using Madame Masque's identity to buy the tape so villains couldn't.
Issue 5: Firstly, him promising to never lie to her, ever, and apologizing for her seeing the, highly disturbing, tape of him brutally killing a Bin Laden/Kim Jon Il Expy. Secondly, at the end, when he and Fury reveal the tape was fake, and made to protect the SEALS who were really responsible for the assassination. She concedes that going through so much trouble to protect some people he's never met makes him a pretty awesome guy.
Issue 6: Clint, having been threatened by a large gang of tracksuit wearing gangsters to leave New York, decides to stay following a What the Hell, Hero? speech by Kate, and after driving them away, then babysits a neighbour's children so she can have some alone time for the first time in a while.
Issue 7: Meta example: Matt Fraction's earnings from this issue will all go completely to supporting those affected by Hurricane Sandy, with him actually begging the readers to make this as painful for him to give away as possible. Comic-wise: Clint and Kate have separate ones: 1) Clint rescuing Gilbert and his father. Gilbert almost drowns when he went to the basement to retrieve some mementos from his mother. He angrily vents about his father for losing everything at the house, but Clint makes him realize that he didn't lose everything (AKA his father). After getting the two to safety, Clint finally learns Gilbert's real name (since he didn't really know). 2) Kate goes out to get medicine for sick folks, but when she arrives at the pharmacy she sees that it is being looted. One of the looters knocks her out and when she comes to, she realizes her bow and gear were stolen. However, the owners of the pharmacy and several other citizens detain the looters until the police arrive. This prompts Kate to call them "my heroes".
Issue 8: Has Clint risking his Avengers status for a girl he doesn't even know the name of, as well as the more subtle one of the opening, featuring Clint playing party games with Black Widow, Spider-Woman, and Mockingbird. Considering the fact that Bobbi and Jess haven't been seeing eye-to-eye due to Bobbi being jealous of Jess and Clint, and that Natasha is usually more serious, it only fuels the, already prevalent, heartwarming sensation on gets from seeing superheroes just hanging out and being normal people.
Issue 9: Has Kate being the only woman visiting Clint that's not looking to smack him around. Once the other women visit Kate, she tries to get to Clint's apartment before Spider-Woman gets there.
Also, Bobbi visiting Clint's apartment. She beats up two bros who are watching the building and worries about what he's got himself into. She might be his ex wife, but she'll always be there to help him.
Issue 10: Kate hitting it off with the Clown, unaware of his true nature. The two even kiss, and he seems slightly upset when he realizes she's friends with his target.
Issue 11: Pizza Dog defending someone from the Tracksuit Bros. Pretty awesome for a pooch with one eye, and fairly sweet.
And when it looked like the smaller dog who was his companion rebuffs him as she enters their apartment building, Pizza Dog slumps a bit until she pops her head out with a huge doggie smile and her tail wagging. Lucky happily follows her inside.
Issue 13: I just didn't want him to hear about it on the phone, is all. I didn't want him to be alone.