Koriand'r / Starfire

Earth-One / Post-Crisis / New Earth
Initially denying his feelings for Kori, Robin realized how much he loved Starfire when her life was threatened by Blackfire during an outer-space adventure ( New Teen Titans #23-25, New Teen Titans Annual #1, 1982). In the heat of the battle, Robin’s burgeoning feelings for Starfire became obvious. The two fell in love and became a couple.
 * 1)  Dick Grayson / Robin / Nightwing - When Koriand'r first encountered teh Titans, In an attempt to learn English, she absorbed the language by planting a kiss on Dick. This left him flustered, but meant nothing romantic at the time. (New Teen Titans #2, 1980)

It was later revealed in a retcon that Barbara had come to Dick’s apartment once in an effort to kindle something between them, only to be greeted by Kori in her underwear, then walking away crying.

The couple faced their greatest challenge when Starfire was forced into an arranged marriage to quell a Tamaranean civil uprising. While Starfire saw this as a marriage of state, Dick felt betrayed and left his alien love on Tamaran (New Teen Titans, vol 2, #15-18, 1986). Stafire eventually returned to earth, and reconciled with Dick once he learned she did not take the traditional Tamaranean wedding vows (#39, 1988).

The shape-shifter Mirage even kidnapped and impersonated Starfire, causing strain in her relationship with Nightwing. Impulsively, Dick proposed marriage to the tempestuous Tamaranean, desperately hoping to mend their relationship.

Dick was off-planet when Barbara was paralyzed. When arrived and heard the news, he came to her apartment, and the two fell into an embrace, sleeping together. Afterwards, he gave her an invitation to his and Kori’s wedding, causing an infuriated Barbara to kick him out. This type of behavior was later attributed to an evil possession on Dick’s part.

Dick and Kory's wedding ceremony was interrupted by Raven, now reborn as an evil avatar of her father, Trigon (#99-100, 1993). Starfire was implanted with a demon “seed” by Raven, which caused her to leave Earth and go on a spiritual journey (NTT#114 & Showcase ’94 #11, 1994). Thus, the long-standing relationship of Nightwing and Starfire was at an end, with neither party acquiring much closure.

2.  Ph'yzzon  - Starfire found brief happiness in a marriage to the binary-powered alien known as Ph’yzzon (NTT#127-130, 1995). But he died while trying to protect New Tamaran from the Sun Eater (Final Night Preview, 1996).

Kory later returned to Earth. Although they have succumbed to old passions more than once, the pair have decided to remain good friends above all else.

New 52
She has also slept with Jason Todd, but as a Tamaranian with different sexual values, this doesn’t appear to  mean much.
 * 1)  Dick Grayson / Robin / Nightwing  - I believe she has a similar history with Dick in the New 52. After leaving Earth for a while, she says she that Tamaranians start losing their memories of other worlds after a time, that her memories are fading, and she can no longer remember his name. This later appears to be an exageration, if not a bold lie.
 * 2)  Roy Harper  - She and Roy have slept together, and apparently have a continuing tension.

Teen Titans Animated Series

 * 1)  Dick Grayson / Robin  and her have a continuing romantic tnesion in this series.

DC Animated Movie Universe

 * 1)  Dick Grayson  and her have a romance in this Teen Titans: The Judas Contract.