Although Natasha doesn't have any living family members, she did have relationships with other heroes. Including...

Winter soldier with who she met in the Red Room when he trained her, they fell in love but where taken away from each other and they were brainwashed to forget.

Red Guardian (Alexi Shotstakov) was formerly the husband of the Black Widow when she was given by the Red Room implanted memories if her being a ballerina and to keep her loyalty true. Although the Red Room later told Natasha that was killed which wasn't true.

Hawkeye, also had a relationship with Natasha. She persuaded him to join her on her work and they both fought Iron Man, they almost won until Natasha was badly hurt. They both continued to work but when Natasha was captured by the Red Room and brainwashed again. She breaks free from the psychological conditioning with help from the Avengers.
Although in the movies, it is suggested that Hawkeye was sent to kill her but made a different as said by Natasha herself.

A certain blind hero who was named Daredevil met Black Widow in New York and had a relationship. They had a long relationship but soon they broke up.

In Avengers: Age of Ultron, she had a romance with Bruce Banner.

(Personally I thought it was very sudden and their relationship wasn't built up unlike Natasha and Steve's relationship was in CA: TWS, but I would love for her not have a romantic relationship and be independent as she was in the comics. Although I do love Scarlett Johansson's portrayal) Sorry for my babble.

She also had a relationship with Steve Rogers in the animated movie Ultimate Avengers (2006) and had a child in The Next Avengers (2008)

There is quiet a bit I missed, but I got the main facts hopefully, thank you for the question.