As my dad liked to say: “Nobody ever notices that this little old lady shows up in town, and someone dies, every time.”
The various Scooby Doo shows all of course centered around a team of private investigators, albeit one that supposedly concentrated on paranormal stuff.
Second or third season of Bones has Hodgins and Angela hiring a private investigator to track down Angela’s long-lost husband. As an added service free of charge, the investigator does her damndest to convince Angela to go back to her husband, and failing in that pursuit, informs Hodgins of Angela’s loyalty to him and complete disinterest in the other guy.
Babylon 5 has Micheal Garibaldi becoming a private investigator in the fourth season, and even when he was still the chief of security, he would pick up off-the-clock mysteries to solve because he’s an adventurous OCD kind of guy.
A previous poster mentioned Veronica Mars. This show in fact had three private investigators: Keith Mars, his daughter Veronica, and a sleazy guy across town who charged less than Keith did.
The Animatrix short “Detective Story” had a private eye hired to track down Trinity. That one was totally sweet.
Firefly arguably featured various folks you could call PIs, but they were usually billed as mercenaries or bounty hunters (if they were called anything that nice),
And of course, Cowboy Bebop had the Cowboys, otherwise known as your friendly neighborhood bounty hunters. On that show, they often did detectivey things in the persuit of their marks.
From what I’ve read, one of the bigger private eye firms, the Pinkerton Detective Agency, nowadays does things like hiring out security guards for business places or college campuses (the school I went to before I enlisted had guards employed by a firm that was owned by the same people who own the Pinkerton agency nowadays). Granted, they may only investigate unlocked office doors and lights on after business hours and that sort of thing.