Lover Not a Fighter

Sometimes women go for the strongest, the bravest, the most competent badass in town, on duty at all times to rescue them from supervillains, fight off potential love rivals with extreme prejudice, and carve their face on the moon on Valentine's day. ...And sometimes they just want the normal guy. Thus, the Non-Action Guy or male chick of a group will very often have the most luck with the opposite sex, and it may be their most obvious quality. This may be to make them seem manlier in lieu of their companions' capacity for violence, to take advantage of the fact that viewers will identify more with more normal characters, or merely to give the audience a good reason to root for them. If the series has an active fandom, this character is the one with the widest variety of pairings in evidence.

May be paired with his opposite, the Hot Amazon.

Examples of Lover Not a Fighter include:

Advertising

The Most Interesting Man in the World is a lover, not a fighter, but he's also a fighter, so don't get any ideas.

Anime and Manga

Black Lagoon. Revy (who, it is worth noticing is one of the best fighters on the show, has had several guys make passes at her. Admittedly none of the ones we see try to chat her up are action guys, but given her appearance and the general population of Roanapur some Badass guy must have made a move. The only guy she's ever shown the slightest interest in is Rock.

Comic Books

Wee Hughie is the least murderous of all The Boys, and seems to be the only one with anything approaching a normal love life.

Film

In the movie Van Helsing, the Plucky Comic Relief (and Q) ~~monk~~ friar manages to pick up a woman more or less by accident. By comparison the titular character kills his Love Interest by accident.
Who Framed Roger Rabbit?:

Jessica: My honey-bunny was never very good behind the wheel.
Eddie Valiant: A better lover than a driver, huh?
Jessica: You better believe it, buster.

Literature

Aramis of The Three Musketeers was the less brutal and had the most luck with women. And then D'Artagnan arrived, who did both.
Compare Don Quixote's love life with that of his non-action servant and sidekick, Sancho Panza.
- Sanity Has Advantages.

Live Action TV

Gaius Baltar of Battlestar Galactica is an unabashed Lovable Traitor and Dirty Coward, but he gets easily the most play of any man in the series. Must be the accent...
The geeky, harmless Wash of Firefly is this trope - he's married to Zoe, the Hot Amazon. Simon also qualifies, but only after Serenity.
In a roundabout way, this trope is ascribed to the titular character of Merlin. After Guinevere is arrested for witchcraft, Merlin makes a bid for her freedom, leading everyone to believe that he's in love with her. On trying to convince Arthur to help her find the real culprit behind the magic that Gwen has been arrested for, Morgana tells him that Merlin is "a lover, not a fighter" - though whether she actually believes this or not is debatable.

Music

Michael Jackson cites the trope's name in one of his duets with Paul McCartney, "The Girl Is Mine".

Video Games

"I'm a hugger, not a fighter. Take off, eh!"

Web Comics

Elan of Order of the Stick, as lampshaded at least once.
Marena, the resident Lunar Exalted in Keychain of Creation, seems to be this for the the entirety of the first chapter and much of the second, an assumption made in large part due to her apptitude for Manipulation, shapeshifting and promiscuity being juxtaposed with several instances of her outright stating that she is useless in a fight. It should be noted, however, that Marena also happens to be a bloody liar, and as such failed to mention her Deadly Beastman Form(tm) until it was dramatically appropriate, so this is a bit of a subversion.
Geoffry of Wiglaf and Mordred is Happily Married, but it is mentioned that if Janus ever dropped dead, over half the women in the Evil Lair would be fighting over him.

Web Original

Tucker of Red vs. Blue declares himself to be this often. Amusingly enough, the reverse is probably true—he's actually one of the best non-Freelancer fighters in the series, and his skill with women is largely an Informed Ability... with the information coming only from him.

Western Animation

Sokka of Avatar: The Last Airbender- Sure, he can't bend elements with his mind, but he gets at least a Ship Tease with nearly every female character, and he eventually ends up becoming a Badass Normal.