In Bodyguard (UK 2018), PPO David Budd is assigned to Home Secretary Julia Montague after the country increases security of government officials following a foiled terror attack. In the aftermath of an attempt on Julia's life, she and David have Glad-to-Be-Alive Sex. This turns into a series of one-night stands which present complications for both parties. In addition to being a violation of his professional ethics, the truth would destroy David's already strained marriage. Julia has aspirations to be Prime Minister, but her counterparts see her as too aggressive. The reveal of a sex scandal with her married protection officer would be seized upon to block her political. After Julia is killed in a bombing, the illicit relation is used to question David's actions and motivations.
King Renly Baratheon is the object of affection for both Ser Loras Tyrell (an unusual reciprocal example because they form a same-sex couple) and Brienne of Tarth (a rare gender inversion of the trope), who are members of his Kingsguard. Brienne later rues the fact that she only held him once, as he was dying. Jaime later figures it out.
And, "The King of the Friendzone" himself Ser Jorah Mormont qualifies after he develops one for Daenerys, even if All Love Is Unrequited. He takes this trope to the furthest, being exiled by his beloved twice and threatened with death, he takes extreme measurements to return to her and beg to become her bodyguard again.
Daario Naharis is also one of Dany's bodyguards, and she keeps him close partly to have him as her lover.
In the first two seasons, Sandor Clegane served as Joffrey's bodyguard and his duties contained guarding also Joffrey's betrothed Sansa, for whom Sandor seemed to have some mixed feelings.
In Heroes, this APPEARED to be the case for Peter and Claire. This was squashed immediately upon the reveal that they're actually each other's long-lost uncle and niece. Of course, this didn't actually stop the shipping or the sexual tension between them. The fact that the actors portraying the two got involved surely contributed to the shipping and tension. Hayden's young age (relatively) added some risque' spice, as well.
In Charmed, the Powers That Be mandate a strict law against Whitelighters falling in love with their Wiccan charges. But naturally, this was dealt with offscreen and waived in the case of Piper (main character), who married Leo and later on in the series even got to have a child. Even with Piper's mom and Sam, another whitelighter, having an affair and ended up with Paige.
In The West Wing, CJ Cregg and her bodyguard Simon Donovan (better known asGibbs) when she's under Secret Service protection while being stalked. When they catch the guy CJ needed protection from in the first place, Simon is promptly shot and killed. Thanks, Aaron Sorkin. Thanks a lot.
In Terminator: The Sarah Connor Chronicles, while there isn't anything romantic going on yet between John and Cameron, a lot of John's growing attachment and protectiveness of her is stemming from her own protectiveness of him. Then there's the second season finale, in which John, against the advice of both his mother and Agent Ellison, travels into the future to retrieve Cameron's chip. Cue Fangirl Squee!.
Chuck and his bodyguard, Sarah. Chuck has a massive crush on Sarah. Sarah seems to entertain the idea of a relationship with Chuck, but there's the whole CIA thing getting in the way, and it's causing a few problems. Especially considering that they have to play the roles of boyfriend and girlfriend and occasionally a married couple on certain missions. Less overtly (this is a family show after all), the other bodyguard in Chuck's life...John Casey, played by Adam Baldwin. Scroll up this page a tad...
In Tin Man fandom, DG/Cain plays out like this most of the time. DG is Princess of Oz, named for her ancestor, Dorothy Gale. Cain is a Badass Normal by Ozian standards, a commoner, and a law enforcement man/soldier by trade. Sweetening the deal is that, in the first part of the series, Cain's former boss forced him into a promise to "not leave her side at any cost."
In an episode of The Equalizer Robert McCall chews out Mickey Kostmeyer for sleeping with a Swedish foreign student he was supposed to be guarding, pointing out that if the killers had chosen to strike at that moment they both would have been killed.
G'Kar may have been trying to invoke this trope when he insisted that the rogue telepaths leaving B5 have Narn bodyguards. Given G'Kar's attempt in the premiere episode to get telepathic genetic material for the Narn race via the old-fashioned mating method, one wonders if he wasn't trying to set up a few Interspecies Romances.
Lennier isn't a bodyguard per se, but he does have a crush on Delenn and he does consider himself honor-bound to protect her.
As Echo's fourth official handler in Dollhouse, love interest Paul Ballard has one of these, though the crush began long before he actually started work as a bodyguard.
Done much squickier with Sierra and her original handler.
Bones: Although not a technical bodyguard, Agent Booth often says that keeping his partner, Dr. Brennan, safe is his responsibility, seeing as she is not trained as an agent and (for at least part of the series) is not supposed to be carrying a gun. This stance towards Bones' safety leads to much UST and Everyone Can See It.
The Angel episode "Guise Will Be Guise" depicts Wesley getting involved with a girl he's been hired to protect. The guy who hired him apparently knew about this trope, because Wesley was impersonating Angel, who was wanted specifically because he can't have sex. He needed her for a Virgin Sacrifice - as it turned out, he should have started paying attention to this possibility a lot earlier.
In Buffy the Vampire Slayer, Angel was originally supposed to act as a secret protector for Buffy the Slayer - but, while watching over her, fell in love.
Inverted in season 5 of 24, with First Lady Martha Logan, fully disgusted with her husband's actions, falling for Secret Service agent Aaron Pierce. Season 6 finds the Logans separated (divorced?) and Pierce retired from the Secret Service and romantically involved with Martha.
The NCIS episode "Defiance" had a character of the day fall in love with McGee. She then used this to catch him off guard in order to stage her own abduction, and the episode leaves open whether or not she was acting the entire time.
This is basically the premise of Amor en custodia, an Argentinean telenovela which has been remade in other countries, included México, where it was remade twice: One time in TV Azteca and Its fourth remake, which is currently on air in Televisa under the title "Amores Verdaderos"
Starsky & Hutch: Hutch gets into one of these with a visiting Russian ballerina who's received death threats.
Person of Interest: Reese and Sophia were clearly going down this trope's path, as well as with other women Reese protects, but it's always pretty one-sided.
Miami Vice: Crockett meets his second wife Caitlin Davies because she's testifying against her former manager for payola and needs protection. At first, she dislikes him, calling him the "fashion police" and asking him, "What are you going to protect me with? A blowdryer?" They don't resolve their differences until after he saves her from hitmen.