Angel (the one with the children's show puppets) had an edutainment puppet named "Ratio Hornblower".
Monday Mornings had a nice Actor Allusion. Ioan Gruffudd played a doctor and his boss asked him several times if he was familiar with the concept of "captain of his ship".
Star Trek took a lot of inspiration from the Hornblower books, and they do put in a few nods:
In one episode of Star Trek: The Next Generation, Data is put in temporary command of a ship called the Sutherland where he proceeds to act as a very straight-faced Military Maverick on a blockade.
Jake Sisko, son of The Captain in Star Trek: Deep Space Nine, is a writer. Whenever the camera peeks in on the manuscript he's editing, though, it's text from Commodore Hornblower.
Literature
The Expanse: One of the ships in Michio Pa's fleet is named Hornblower.
The Honor Harrington series is explicitly "Hornblower In Space", with the first novel dedicated to C.S. Forester and its eponymous protagonist deliberately sharing the H.H. initials. In one of the novels, Harrington is reading a Hornblower book herself.
One book in the Alan Lewrie series (depicting a much less heroic naval hero) has the main character notice of a tall, thin, and melancholy-looking lieutenant in a threadbare uniform at the Admiralty during the Peace of Amiens—a tacit reference to Hornblower, who had no position on a ship and was under pay stoppage.
Hornblower is alluded to several times in Sten Nadolny's pseudo-biographical novel of Sir John Franklin, The Discovery of Slowness. The Lydia makes a brief cameo in port and one of the characters, Franklin's childhood friend Sherard Lound, is even revealed to have become Hornblower's Lieutenant Gerard, and finally gets a Bittersweet Ending.
The third Ciaphas Cain book mentions a navy commander named "Horatio Bugler."
Harry Dresden, though he knows how to steer a boat, mentions that he's no Horatio Hornblower.
Harry Harrison once wrote a short story entitled "Captain Honario Harpplayer R.N.", in which Harpplayer's new recruit is a Little Green Man, but he doesn't realise this because, instead of being tone deaf, he's colour-blind.
In Age of Pirates II, a character named Horatio Hornblower will aid the player if they ask him the right questions.
Web Original
It's a running joke on this very wiki to call Honor Harrington novels Horatio Hornblower IN SPACE!
In a parody rap song "Jane Austen is My Homegirl (Downton Abbey Rap)" by Pretty Darn Funny, one part says, one part referenced the dashing sailor. Watch it here.
My friend loves Phillip but, I'll have to show her, no man stills my heart like Horatio Hornblower.
The title of the Bugs Bunny cartoon Captain Hareblower is a reference to Hornblower.
Real Life
During his acceptance speech at the 1980 Democratic National Convention; incumbent President Jimmy Carter unintentionally referenced the books when he, during a tribute to former Minnesota Senator and former Vice-President Hubert Humphrey; accidentally called the late Senator Hubert Horatio Hornblower.