The Twilight Saga: In Eclipse, Bella and Edward's relationship is compared to Cathy and Heathcliff's.
In Save the Enemy, Zoey remembers reading Wuthering Heights before her mother was murdered and her father disappeared.
Things I Should Have Known: In English class, a kid comments that he thought Wuthering Heights was totally incestuous, which leads the class into a discussion on whether it's okay to think your cousin is hot.
Live Action TV:
In 'Allo 'Allo!, the flight lieutenants Carstairs and Fairfax discuss that they should surrender to Germans than suffer hidden with incompetent Resistance members like René. They say they might want to get to a proper camp and get a part in production of Wuthering Heights. One of them says he would make a good Heathcliff, though the other says he might be asked to shave his moustache and play Cathy.
The book is discussed in Friends when Phoebe is taking literature classes.
Monty Python's Flying Circus: One episode had an adaptation of Wuthering Heights with all the characters making flag signals.
Music:
Genesis's 1976 album Wind & Wuthering takes part of its name from the book's title, and two (consecutive) tracks on the album are titled "Unquiet Slumbers for the Sleepers..." and "...In That Quiet Earth", as a reference to the book's closing line.
Kate Bush's 1978 song "Wuthering Heights" on her album The Kick Inside, sung as by Cathy to Heathcliff.
Jim Steinman, writer of "It's All Coming Back to Me Now" which was famously recorded by Céline Dion, has cited Wuthering Heights as the inspiration.
Bree Sharp's 1999 hit song "David Duchovny" includes lines
David Duchovny hovering above me / American Heathcliff, brooding and comely.
Death Cab for Cutie's 2008 song "Cath...", which is fairly transparently based on Wuthering Heights, but in their own style.
Theatre
In Mary Mary, Mary wistfully recalls that, when she was in high school, she had romantic fantasies about being Catherine Earnshaw.
"I used to dream that somewhere there was a strange, dark man whose heart was quietly breaking for me. On rainy nights I'd open the window and imagine I could hear him calling—'Oh, my wild, sweet Cathy!' The colds I got! And of course the only dark man I ever saw was the middle-aged dentist who used to adjust the braces on my teeth."
Video Games
As part of the main cast of Limbus Company all being classic literature references, there's Heathcliff. He's a bitter, stormy-tempered man from an impoverished background that has some tragic romantic entanglement with a woman named Catherine. The game's English translation makes his dialogue sound extremely British as a further nod to his literary inspiration.
Web Animation:
In Episode 18 of The Most Popular Girls in School, Mackenzie Zales references reading this book on a Nook (or her not wanting to, thereof).