Hawkgirl (Shayera Hol) is the love interest of Hawkman in some continuities.
In ancient Egypt, princess Chay-Ara and her husband Katar Hol were spouses that stumbled upon Earth. They were later killed by the evil Priest Hath-Set by an knife made of Nth Metal, because of the weapon's properties where instead of dying and going to the afterlife, she would be constantly re-incarnated and take on the mantle of Hawkgirl.
Live Action Media
Legends of Tomorrow
In Animated Media
DC Super Friends
Hawkwoman (Shayera Thal) appears in Young justice as a member of the Justice League. She is a Thanagarian, and married to Hawkman.
In the ancient past, Shayera and Katar were thanagarians that stumbled upon Earth (Chay-Ara and Khufu), where they were revered by the Egyptian tribe, however they were soon killed by the evil priest Hath-Set with an knife made of Nth Metal. due to the weapons properties, instead of permanently dying, they would be destined to constantly reincarnate, meet each-other, and be killed again.
Their relationship in the DC Universe can vary, as Katar Hol/Hawkman can become her partner, love interest, or spouse.
John Stewart/GreenLantern (DCAU Justice League only)
In this continuity, Hawkgirl developed a relationship with John Stewart during her time with the League. The two started off rocky as they constantly bickered, but they eventually found common ground through their shared military/police background. This relationship came full circle in "Wild Cards", where she revives him and takes him to the Watchtower to recuperate, discussed the state of their relationship, and they ultimately shared a kiss at the end. Unfortunately the event of "Starcrossed" put a considerable strain on their relationship, where Hawkgirl is revealed to be both a scout and engaged to Hro Talak.
They would meet again in Unlimited, but choose to settle for being friends, while finding out his new relationship with Vixen (sparking a friendly rivalry with the latter). In "Once and Future Things", her and John would have a son together. In "Ancient History", it was revealed that Shayera and John (as Chay-Ara and Bashiri) were destined soulmates. In the end, the fate of their relationship was left ambiguous in the TV series, since her and John were never shown hooking up again in the series.
In the Batman Beyond comic, Rex Stewart (Warhawk) mentioned that Shayera and John would eventually retire from the Justice League and move to Africa, where they conceived young Rex and taught him various things (via literature, fighting, Nth metal gear).