I have always been a big fan of the Cap/Diamondback relationship. Its a shame Rachel isn't used more.
Hawkeye/Moonstone is another great one. It started as Karla just trying to get a handle on Clint to be able to manipulate him when he took over the Thunderbolts, but they developed a real relationship which led her to come the closest she ever came to legitimately reforming.
The Ant-Man/Beetle relationship in Scott Lang's solo series was fun too. It didn't get anywhere near as serious as Cap/Diamondback or Hawkeye/Moonstone, but it was fun seeing Scott in this relationship that he knew was a bad idea...but he was enjoying too much to let it go.
This one isn't a romantic or sexual one, but the Squirrel Girl/Kraven relationship from Squirrel Girl's solo series was something special.