When this troper saw the movie, he really wondered: How could any man, horny or not, fall for such a stupid act? One should think that a little child would be able to look through her charade.
Perhaps the tagline of another Michael Douglas movie, Disclosure, says it all; Sex is power. Douglas' detective is so enamoured with this woman, so enticed by her, that he basically can't see the forest for the trees, despite being a detective. Tramell's meant to be the perfect femme fatale, and that's how the trope works - older movies are full of men confounded by attractive, dangerous women.
Also, Nick's history suggests he likes to live life on the edge and engage in reckless behavior. He may not care that Catherine is perfectly positioned to kill him. The thrill of courting death could be a powerful rush for him. As she herself puts it, "Nicky got too close to the fire. Nicky liked it."
Plus which, he believes that playing Catherine's game will help him nail the killer. If it's not the sexual challenge that excites him, it's definitely the intellectual one—he thinks he's a step ahead of her in regards to the murder investigation, outright telling her "I'm in love with you, but I'm going to nail you anyway", and expects to come out the victor one way or another.
The women aren't so smart either—Roxy stays with Catherine even though Catherine openly cheats on her and encourages her to watch her coupling with men, deliberately arousing her to violent levels of jealousy. In Real Life, regardless of gender or orientation, this would be an incredibly unhealthy and downright emotionally abusive relationship. And if Catherine is telling the truth about Beth—that Beth is the one obsessed with her—Beth herself is still entangled someone that she knows is lethally dangerous.