I feel like one of my favorite aspects of Romanogers (specifically in the MCU) is that they make each other better without even trying.
Natasha starts off with her usual ways of keeping secrets for Fury, and putting distance between herself and most others. But during the Winter Soldier movie, we start to see that mindset start to shift. We see her let Steve in more and more, and thanks to him, start questioning if the way she does things is truly the best way to do it. He shows her things don't always have to be in a gray area. I think the biggest difference is that she starts to trust in herself more.
She was very used to a "spy" mindset, which is to never let the mask crack, and to never question the mission. But she start questioning SHIELD, and starts making plans that SHE thinks is best. And the movie ends with her laying out it all for the courts to hear, and saying that the world needs heroes. No mask, no defending the mission, just that heroes can do what the government can't. There were multiple factors to this ending, but I think Steve choosing to trust her despite knowing all she's capable of played a huge part. Because he saw the woman behind the mask, and knew that she was someone worth following.
Steve on the other hand, starts off in a similar position. He just lost decades of his life, lost everyone and everything he ever knew, and went right back into the fight. He is much more friendly than Natasha was, but equally just as guarded. He tries to make friends outside of SHIELD, but aside from Sam, he can't really connect with anyone from the "outside." Within SHIELD, it's worse, him turning down multiple opportunities to truly get to know the people he's working with. He sees himself as a soldier, someone who protects people and completes the job, no matter the personal cost. There's no room for genuine relationships, especially in an organization with as many secrets as SHIELD
This completely changes once Nick Fury is "killed" in his apartment. He's forced to go on the run, and has no choice but to rely on other people. Most notably, Natasha, someone who is filled to brim with secrets. He slowly starts to get closer with her, with her teaching him that the world isn't always black and white. He also gains someone who sees him as more than just a soldier, or a means to an end. She put her trust in Steve Rogers and his good heart, and that made him gain a friend. He can't replace what was lost, but he can move forward. And at the end, he doesn't confront Bucky as a soldier, he confronts Bucky as Steve Rogers, an old friend.
And I can honestly keep going with all the moments that show how much of an impact they had on each other, but these were just the ones I can think of. Thank you for coming to my TED talk.