Roy Harper

Earth-One / Post-Crisis / New Earth
1.  Donna Troy  - Serving together as Teen Titans, these two shared a first date, and a first kiss. (Teen Titans #19, 1967, Teen Titans: Year One #5, 2008).

The two were clearly an item when the Titans reunited years later (Teen Titans #44 (1976) - 53).

This relationship was apparently over by the time of the next incarnation of the Titans series came about. (New Teen Titans #1 (1980).

2.  Cheshire  - The history of this hero-and-villainess' relationship started with one of Roy’s undercover missions for the government. His assignment was to track down Cheshire, gain her confidence, and hand her over to the authorities. But plans changed when Harper fell in love with Cheshire and she with him. Their one night of passion left Jade pregnant, as Roy vanished into the night. (flashbacks in New Teen Titans, vol. 2, #21

Cheshire revealed one of the Titans had fathered her child. (Tales of the Teen Titans #51-52, 1985), She reveals the full truth later, shouting. “Speedy — my lover, and the man who fathered my child! And I wondered what would happen once I tracked you down. Once I stared into your eyes. And now I know exactly what I’m going to do. Roy Harper, I’m going to kill you! Jade failed to make good on her threat, admitting Roy Harper was the “one weakness in my life.” She then allows Roy to hold his daughter Lian for the first time.(NTT #20-21)

With the help of Nightwing, Speedy later freed Lian from Cheshire’s guardianship. Once again, Cheshire’s feelings for Harper led to her own undoing, as she cursed herself for loving the amorous archer. (Action Comics Weekly #613-618, 1988).

Donna and Roy rekindled things years later (Titans #1-25, 1999). Donna’s memories had been mystically restored, and she was questioning her own identity She entered into a wild affair with Roy. Once fully restored in Titans #25, Donna broke it off, admitting that she had just been looking to test her boundaries.

Cheshire comes into conflict wtih the Titans again at later times, and is apprehended (Titans #21-22, 2000)Her attempted prison break-out is witnessed by a visiting Lian. Realizing Jade was well beyond redemption, Roy was forced to take a heart-breaking stand against her (Titans #30)

Years later, after Donna was brought back from the dead, she and Roy admitted they still loved each other, even if no relationshp came of it.

Roy also slept with The Huntress.

3.  Kendra Saunders / Hawkgirl  - After becoming Red Arrow and joining the JLA, Roy finds a mutual attraction with his new teammate, Hawkgirl. Although she is seemingly destined to always end up with Hawkman, while Hawkman was having his own tension with Power Girl, Kendra and Roy end up becoming something of an item.

Roy's daughter Lian was later killed during a brutal attack on Star City ( Cry For Justice #5-7 [2009-2010]), leading an enraged Jade, now more cruel and sadistic than ever, to attack her former lover (Rise of Arsenal #3-4 [2010]).

New 52
 Starfire  - Roy and Starfire have slept together, and apparently has a romantic-tension-thing going on with her.

Rebirth

 * 1)  Donna Troy  and he got back together for a while (Titans: Rebirth), but it didn't last long.

Arrowverse
Eventually, Roy and Thea are reunited, and become engaged.
 * 1)  Thea Queen  - Roy first comes into the Arrowverse as astreet urchin who snatches the purse of Thea Queen sister of Oliver Queen. She tracks him down to retrieve it, and the two forma  romantic bond. (Roy is also the object of the affections of his fellow street urchin “Sin,” but despite this, she and Thea become friends). After Roy’s life is saved by the vigilante The Arrow, he comes to idolize him. He eventually discovers him to be Tha’s brother Oliver, and is trained to be his sidekick. Thea discovers that he has been lying to her, and disgusted at being lied to by many in her life, leaves town, where she trains with her birth father, Malcolm Merlyn. She returned after Roy had become the vigilante Arsenal,  and Roy experienced tension for months before getting back together. When Oliver Queen was outed as the Arrow, Roy framed himself to instead by known as the true identity ast he vigilante. The team then faked his death in prison so he could live on the lamb. Eventually, Thea came to him, and they spent the night together. The next morning, however, he had left her with a note saying that he didn’t want such a life together, and encouraging her to become the newest member of Team Arrow (which she did, becoming Speedy)