Fatal Attraction

Sam Spade: Haven't you tried to buy my loyalty with money and nothing else?

Brigid O'Shaughnessy: What else is there I can buy you with?

—The Maltese Falcon

Now and then a detective will be strongly attracted to someone connected with a crime. She (it's usually a woman) may at some point in the episode become the Damsel in Distress, but if not, she's either the perp or will be suspected of being the perp. If she did it, the detective will be reluctant to believe that she's capable of such a thing until the evidence is completely damning; if she's a Red Herring, the detective will confront her prematurely and lose any chance of a romance with her. Sometimes overlaps with Femme Fatale, but more often she's perfectly nice and sweet until she turns around and holds the detective at gunpoint.

Frequently turns up in the first episode/book of a series, with the implication that the detective's sense of betrayal or loss is what hardens him and forms him into the character we come to know. (Details vary: he might become a commitment-phobic womanizer, a celibate justice machine, or just an all-around cynic, but in any case it's all because of her.)

For the idea associated with the movie titled Fatal Attraction, see Woman Scorned.

For the man (and it's usually a guy) who seems to serially end up in these sort of situations, see Fatal Attractor. This trope is similar to Dating Catwoman, but riskier.

Examples of Fatal Attraction include:

Anime & Manga

Outlaw Star had one Tear Jerker of an example, which is impressive, since it was also a Puppy Love. A girl Jim meets and falls for turns out to be the pilot of the ship sent to kill them - but neither ever realizes the other's identity, and both go into combat looking forward to their date. After the fight, Jim doesn't know why she didn't come...
Lyle "Lockon Stratos" Dylandy and Anew Returner in Mobile Suit Gundam 00.
Reversed in the Cowboy Bebop episode "My Funny Valentine", where Faye is initially attracted to Whitney Haggis Matsumoto, but he turns out to be a petty con artist who was manipulating her into taking on his debts.
A slightly weird Gender Flip in Darker than Black: Hero Antagonist police chief Kirihara falls for Hei in his Nice Guy civilian persona, not realizing that "Li" is actually the superpowered assassin she's been chasing. However, she probably should have, seeing as she connected the two in episode 18 and got quite a few hints later during the most-of-a-day they were hanging out together. Since she did eventually figure it out, she probably realized it earlier but didn't want to acknowledge it.
- It got even "better" in Shikkoku no Hana manga. Misaki first gave Kanami's teasing a blushing "panicking confirmation", later when she once more was a little too late to reach Hei—this time without waving guns, just calling "Li-kun!" and Futile Hand Reach—she was clearly in pain.

Comic Books

Batman repeatedly falls for Catwoman. And he's with Talia, the daughter of Ra's Al Ghul. It's pretty obvious it's not going to work out.
- This happens a lot with one-shot relationships for Batman. If Bruce Wayne is dating someone who isn't a main character, and it seems serious- She's either a villain or she's going to get fridged. The villain from Gotham After Midnight was actually Genre Savvy enough to make herself a potential victim, seduce Batman, and then fake-fridge herself.
Ava Lord from Sin City does this to a cop and a PI in A Dame To Kill For in order to manipulate them.

Film

The ur-example is probably The Maltese Falcon and the ending scene where the Femme Fatale being led away in handcuffs while saying she really loves the detective is often in these examples via Popcultural Osmosis.
The (double) crux of the backstory in The Three Musketeers 1993 - Athos (Kiefer Sutherland) married the former Lady de Winter, only to turn her over to the authorities when realizing she'd been condemned for murder - then realizing she probably HAD been innocent - but was, by the time he met her again, guilty of far worse things. And right after they sorted things out, she DIED. On purpose. To avoid being executed.
A rare male example: In the film The Third Man, the protagonist arrives in Europe to discover that the man he's come to see is dead, and the police were investigating him. The protagonist spends the movie convinced that his friend must have been innocent, and was the victim of some underhanded police conspiracy. He learns later that not only is the man still alive, but he's an amoral Manipulative Bastard, responsible for everything the police believed him to be.
Basic Instinct is all about this trope.
A non-detective example, arguably, is Casino Royale.
The Al Pacino/Ellen Barkin film, 'Sea Of Love', is of the falsely accused variety.

Literature

The backstory to The Three Musketeers has Athos realizing his wife was a criminal and trying to kill her. In the present, D'Artagnan sleeps with Athos' ex-wife unaware of her true identity. She's a murderer and the villainness, so in the end, the musketeers murder her. Yeah, it was a different time.
Happens in every single book of the L.A Quartet. And the cop ALWAYS helps the girl cover up her crimes.
Famously, in I, the Jury Mike Hammer ends up revenge-killing the (very guilty) woman he was all ready to settle down with. This is probably the case that turned him from an ordinary Private Detective into the dispenser of brutal justice we all know and love.
In Tamora Pierce's Bloodhound, Beka, a "Dog" or police officer, is attracted to Rosto, the Rogue (king of thieves).

Live Action TV

Psych: If Shawn shows an interest in a woman, start tallying the evidence against her. Especially if she reciprocates. Once, he actually slept with a competing psychic before he realized that she had committed the crime they were trying to solve.
- Luckily for him things are heating up with Juliette. They're officially together now.
- Also happened to Lassie ( she was only partly guilty) and Gus ( of the Red Herring variety.)
Happens to Tony a lot in NCIS. Once said woman turned out to be a pre-op transsexual.
- Eventually they sent him to get information out of a woman they knew was connected with the crime and she turned out to be a cop.
- In a non-romantic version of this trope, McGee's sister ends up at his doorstep covered in blood and eventually becomes a murder suspect. He's not the one to turn her in, though.
Monk: In "Mr. Monk and the Other Woman", Monk has a brief romance with a woman who resembles his dead wife, but it falls apart when he accuses her of murder. She didn't do it.
- Averted in "Mr. Monk and the Blackout"; Monk goes on a date with a woman who works at the power plant where the blackout started, but she's never a suspect, though she does give him a clue to the criminal's identity.
- In "Mr. Monk and the Bad Girlfriend", it's not Monk but Da Chief, Captain Stottlemeyer, whose girlfriend is a murder suspect. She did it, which came as a surprise since she appeared in previous episodes and was set up to become a recurring character.
Lady Heather's second appearance on CSI. Unusual in that it doesn't become clear she's a suspect until after Grissom has apparently spent the night with her. Doesn't matter, though, as Heather's something of an absolutist and views the fact that he could suspect her at all, no matter what the justification, as a betrayal. (By the way, am I the only one who thinks "Heather" is a silly name for a dominatrix?)
In "The Murder of Sherlock Holmes," the pilot to Murder, She Wrote, Jessica's publisher romances her as she investigates a murder committed at his house. He did it, of course. Her disappointment and moral outrage when she confronts him are a wonder to behold.
Happens to DI Robbie Ross in Taggart a lot.
- Gender-flipped when Jackie goes on a date and sleeps with a man who is later revealed to be living under a fake identity. He didn't kill the men, but he does die in the end.
Happens to Danny Reyes of Shark towards the end of the second season.

Video Games

Max Payne in Max Payne 2 got involved with hired assassin Mona Sax, who was suspected of gunning down a senator. She proved to be innocent of the crime, but that didn't stop another police detective with a romantic relationship with the Big Bad from pursuing her relentlessly and eventually trying to kill both her and Max. She proved to be a very capable ally of Max during the game, and the player actually plays as her at certain points in the game. She doesn't survive the game in the end on the easier difficulty levels, however.
Leon and Ada from Resident Evil practically own this trope.