Selina Kyle / Catwoman

Earth-Two

 * 1)  Bruce Wayne / Batman  - In their first meeting, when she was only called the Cat, Selina caught the attention of Batman, who actually let her get away. From then on, there was constant romantic tension between them. Eventually, he made an honest woman out of her, and they were married with a daughter, Helena. Bruce was later killed in action. Helena  grew up to be the superhero Huntress.

Earth-One / Post-Crisis / New Earth
Later on, she truly does learn his identity, but it is later inadvertently erased from her mind by The Joker, who is attempting to use a mind-control machine to have her tell him Batman’s name and turn her evil. He succeeds in the latter.
 * 1)  Bruce Wayne / Batman  - A similar cat-and-mouse game (pun fully intended) occured on Earth One. Eventually, Selina and Bruce became an item for a time. In an issue after they broke up, she saw him and Vicki Vale together, and became very jealous, even attacking them. This issue seems to show she knows who Batman is, although she never learned, and the issue is seemingly eliminated from continuity.

==== Post-Crisis, their dating history in civilian disguise, and her ever knowing his identity, eliminated from continuity. Eventually, he learns her identity, and after years of sexual tension, the two, even with his identity concealed, become something of an item. This leads to him to divulge his secret identity to her. After a betrayal by a friend, however, he loses this brief ability to trust, making him suspicious of her, and ending the relationship. ====

2.  Ted Grant / Wildcat  and her have had relations in the past.

New 52

 * 1)  Eiko Hasigawa / Catwoman  - Eiko was the heiress to the Hasigawa Family branch of the Yakuza.. After Catwoman interfered with a deal she had been put in charge of, Eiko tracked the woman down and discovered her identity. Catwoman later disappeared and in her place, Selina Kyle took over the Calabrese Crime Family and united the families, with the Hasigawas a prominent hold-out. Knowing Catwoman had been retired, Eiko began dressing in her own catsuit to thwart her father's more morally questionable work, and to spy on Selina.

Eventually, Selina discovered her activities, and the pair allied in trying to use Gotham's organized crime families to do good for the city. The two grew close, and, after a failed assassination attempt resulted in a brush with death for Selina, frightening an Eiko who cared deeply for her, the two shared a kiss.

2.  Bruce Wayne / Batman  - The same basic premise applies. They once again form a relationship, he makes an honest woman out of her,  he reveals his identity, and the two became engaged. The wedding, however, was later called off.

1960s TV Series
Although this version of Catwoman (played by three different actresses) is far more sinister than her comics counterpart, she still shares the same bond with Batman, an attraction that could be love if it weren’t for being on opposite sides of the law.

Batman Returns
This more supernatural (and psychotic) version of the character, is a lowly secretary for mogul Max Schreck, until she discovers his corrupt practices, and is murdered by him by being pushed out of a window. She is ressurected by magical cats chewing on her (yeah, never did make sense, complete with nine lives. As Catwoman, her main goal is to sabotage Scheck’s buildings. She flirts with Batman in costume while also co-conspiring wit the Penguin to kill him. In her civilian identity, she reappears at Schreck’s office feigning amnesia. There she meets Bruce Wayne. and shares a date with him. They later discover each other’s identities, and Bruce attempts to get Selina  to forgo her bloody vendetta against Schreck, but she apparently kills herself (ending her eight life) by electrocuting both herself and Schreck. After the ensuing explosion, her body is to be found among the wreckage, and she is later shown to be alive, enjoying her ninth life.

DC Animated Universe
The same aspect of tension from the comics transfers to the series, but with one of the most definitive exchanges either character has been a part of.

“You can’t deny there’s something between us.”

“You’re right. And I’m afraid it’s the law.”

The Dark Knight Trilogy
In a more comics-accurate portrayal as a jewel thief, Selina starts off her acquaintance with Bruce Wayne by stealing his mother’s pearls, the ones that resulted in his parent’s deaths. He hunts her down and takes back the pearls, but does not turn her over to the police, and she plants a flirtatious kiss on his lips. She also becomes acquainted with Batman, who she betrays to Bane to save her own skin, although she is visibly troubled by the decision. She learns Bruce’s true identity as she watches Bane defeat him. When Bruce then returns from the exile Bane put him in, he still places his faith in Selina, seeing more in her. She ultimately resists the temptation to save her own skin again and helps Bruce liberate the city, later saving his life by killing Bane. As Batman begins to sacrifice himself by flying away with the nuclear bomb Bane and Talia intended for the city, she kisses him.

Batman, and Bruce Wayne, apparently die in the incident. When it is later revealed that Bruce escaped the explosion, he is shown to apparently be in a relationship with Selina, with Alfred seeing them together at a French cafe, her wearing his mother’s pearls.

Others
The same basic relationship/tension is said to exist to some degree between him and Catwoman on Batman: The Brave and the Bold.

Batman’s only romantic entanglement with Catwoman in the Arkham universe is playful flirtation on her part, although she does risk life and limb to save him from the asylum at one point.