Subverted in Suzanne Brockmann's Troubleshooters series book Hot Target where celebrity producer Jane Mercedes Chadwick needs a bodyguard but doesn't want the bad publicity of being in fear of her life so she holds a press conference where she strongly implies that she's sleeping with Cosmo Richter, her bodyguard. Cosmo is very upset and points out that his bodyguard business is fledgling and the implication of sleeping with his clientele makes him look very unprofessional to potential clients who mainly hire him to protect their wives, mothers, and young daughters.
In David Eddings's Elenium series, it's very explicit between Sparhawk and Ehlana. In this case she's his Queen, and with the exception of the backstory period during which he mentored her as a child, any power imbalance is weighed strongly towards her end.
In Laurel K. Hamilton's Meredith Gentry series, the royal bodyguards pretty much also serve as sex slaves to Queen Andais, Princess Meredith, and Prince Cel.
Sandor Clegane is Prince Joffrey's sworn shield, but is more often seen protecting Joffrey's betrothed, Sansa Stark, leading to a Beast and Beauty pairing. Sansa's thoughts seem to be conflicted. She's frightened of Sandor, but he seems to spring to her mind every time sex or kissing is mentioned, and she canonically fabricates a memory of kissing him.
Two members of Renly's Rainbow Guard have the hots for him: Brienne, a large and ugly Action Girl, and Loras, his gay lover.
Jorah Mormont is hopelessly in love with Daenerys Targaryen, whom he serves as part of her Queensguard. She's aware of the situation and repeatedly rebuffs him.
Arys Oakheart, a member of the Kingsguard sent to Dorne with Princess Myrcella, falls in love with Arianne Martell despite his vows. He needlessly dies defending her and their companions at the Greenblood after being forced to yield by the Dornish captain of the guards, Areo Hotah.
Prince Roger The 'March/Prince Roger' saga has the spoilt misunderstood brat, Prince Roger Ramius Sergei Alexander Chiang MacClintock (whew, what a mouthful!) and his Action Girl bodyguard, Nimashet Despreaux, agonize endlessly before finally hooking up in the second book, March to the Sea. This was complicated further by the part where after they finally decided to hook up, Roger went from third to first in the line of succession — meaning that country-girl commoner Nimashet had just gone from 'going to be married to the most redundant junior prince' to 'prospective Empress'. The latter possibility terrified her enough that she immediately broke the relationship off cold — which created some serious tension, given that she was still his bodyguard. Then, Nimashet was given a direct order by her superior officer to reinstate the relationship and become the eventual Empress Nimashet. Even though they know it's a bad idea to fraternize inside the chain of command, they need her to steady Roger because he'd either abdicate to be with her again or else try to rule the Empire alone and end up as Emperor Roger the Mad. (Nimashet is pretty much the only person around who can hold Roger back from massacre once his Berserk Button is pushed, and Roger on some level knows this.)
Kushiel's Legacy: Warrior Monk Joscelin denies himself any attraction, romantic or otherwise, to Phèdre, saying that he can't both be her bodyguard (servant of Cassiel) and her lover, because it goes against his vows, which include a Vow of Celibacy. Granted, in Kushiel's Dart he and Phèdre, ah... paid homage to Namaah. Later in the series, they develop a proper relationship as the Comtesse Phèdre nó Delaunay de Montrève and her consort (read: practically husband) Joscelin Verreuil.
In the second book of the Coruscant Nights trilogy, we find that Padme's eyepatched bodyguard Typho was in love with her, and at her funeral, having seen the autopsy, comes to the conclusion that she was killed by use of the Force. Anakin Skywalker was supposed to be bodyguarding her in Typho's absence. Thus he decided to track down Skywalker; later he assumes that Vader killed them both, so he has to kill Vader. You can imagine how that went.
In the Jedi Academy Trilogy General Wedge Antilles is set to bodyguarding Qwi Xux, an ex-Imperial scientist who had worked on the Death Star, the World Devastators, and the Sun Crusher, cheerfully oblivious to what these projects would be used for. Yes, a general serving as bodyguard to a scientist. They fall for each other, and in I, Jedi this development dismays Corran, since he ships his boss with one of his friends (Who Wedge did end up with in a later novel after breaking up with Qwi).
In Moira Moore's Heroes series there are two kinds of magic users, Sources and Shields, who get permanently paired up. The Source deflects natural disasters while the Shield protects the Source from some kind of backlash that occurs. First person narrator and Shield Dunleavy really likes her Source Shintaro and protects him not only while working magic but tends to protectiveness also in more mundane situations. He in turn makes no attempt to hide that he lusts after her.
The Rifter: Kyle (the Kahlil) is assigned to secretly watch and guard John when John is a child. He does so for ten years, and as John grows up Kyle becomes immensely attached to him, though he wonít allow himself to think that he might be falling in love because he knows he might receive the order to kill John. By the end of the book, Kyle knows for certain that guarding and loving John (the Rifter) are his two purposes in life. Itís both a confirmation and a radical revision of the relationship that the holy scriptures indicate between the Kahlil and the Rifter.
In the Spaceforce series, Prince Ragoth, youngest son of the Taysan Empress, has a personal entourage of three bodyguards from the exclusive Clan of the Imperial Shield. The most recently appointed is Maydith, who is young and pretty. Other characters suspect that the pair are in love, but because of the crippling restrictions of Taysan society, it can never be.
In the Gemma Doyle trilogy apparently it was once pretty common for the Rakshana and the members of the Order they guarded to be lovers. Named examples include Gemma and Kartik (eventually), and Miss McCleethy and Hugo Fowlson. It may or may not be worth noting that neither pairing ends well, but then, what pairing in this series does?
In the Quantum Gravity series, LilaBlack has been hired to bodyguard/spy on Zal, and the first thing that happens when they meet is a love match Game, which pushes them together, along with Zal's general open flirting. They marry.
In the The Compass Rose, magic-users in the military are assigned bodyguards. Kallista's bodyguard Torchay is madly in love with her. Kallista resists, but after being ordered into marriage, eventually requites Torchay's feelings.
The Elfstones of Shannara: Invoked by Rone Leah in Wishsong: he goes along to protect Brin specifically because he has a crush on her.
The Godless World Trilogy: It isn't obvious, but Anyara's bodyguard Coinach seems to be developing a bit of a crush on her, which she may well reciprocate (she looks straight at him when someone tells her she should marry in order to make herself happy).
Hugh Arai for Queen Berry in Torch of Freedom. He's luckier, because she reciprocates the feelings, fires him as her head of security, and drags him off to her bedroom. Possibly inverted, as she fell for him even before he was assigned as her head of security.
Major Andrew LaFollet, head of Honor's Grayson-assigned Steadholder security detail and her personal chief bodyguard, spends most of his life quietly, deeply, and unrequitedly in love with her, even refusing to marry or have children (all but unheard-of on Grayson) in his devotion to her. She's aware of his feelings and regrets hurting him by not reciprocating, but he doesn't seem to consider it a loss.
Anne Rice's Angel Time: Lucky the Fox and his boss, The Right Man have something going on, although it's implied that it doesn't involve sex.
Ari II and her "azi" (essentially slave, though YMMV) bodyguard Florian in Cyteen.
In Andy McDermott's Nina Wilde series, the titular Adventurer Archaeologist and her ex-SAS bodyguard Eddie Chase slowly fell in love and married over the course of their adventures. The romance is subtle and only made in passing mentions since their main focus is trying not to die preserving rare artifacts.
In the Kris Longknife series, there are some very strong hints that Kris' bodyguard Jack is in love with her.
In Cerberon, Margaret becomes attracted to George after he volunteers to be her escort for her journey to America. He is oblivious to her attraction until she mentions she wouldn't mind his intimate attention.
In Star Trek: String Theory, the Back Story for ally character Ziv and minor antagonist Sem involves this trope; Ziv was Sem's bodyguard, and in violation of their people's custom they had a sexual relationship.
In Shadow of the Red Vixen Alinadar develops one on Lady Sallivera, though it's not requited until "Shadow of her Sins", and had another unrequited one for her previous mistress The Red Vixen. It turns out towards the end of "Shadow of the Red Vixen" that Melanie was trying to invoke this when she hired Ali to be Salli's bodyguard.
In Lucky by Jackie Collins, the heroine, a teenager at the time, falls for and when she's old enough begins a relationship with her bodyguard. It ends badly.
In the Black Blade series, Lila Merriweather and her employer's son, Devon Sinclair.