I like connections. I like connections between the literature and culture of Shakespeare’s time, and his work, and I like finding how people have played with Shakespeare’s work ever since. One of the most fun connections between Shakespeare and popular culture that I’ve run across recently is the Dr. Who episode “The Shakespeare Code.” Dr. Who is an important part of modern British pop culture, and Shakespeare has been an important part of the culture for a long time, seeing the episode play with the quotes and allusions to Shakespeare's life and works (as well as to other cultural references) is great fun whenever there's a new reference that you catch.
Wikipedia has a long list of the references to Shakespeare and his work in their article on “The Shakespeare Code” episode. Some of my favourite references are described here
I feel like I ought to be doing some analyzing here, but I'm not quite sure how you analyze something like this. I do see that Shakespeare taking up so much time in a popular modern TV show episode is both proof that people still, to some degree, appreciate Shakespeare and also that seeing the Shakespeare references gives them a new way to appreciate and remember his works.There is a running joke throughout the episode in which the Doctor creates an apparent ontological paradox by inspiring Shakespeare to borrow phrases that the Doctor quotes from his plays. Examples of this include the Doctor telling Shakespeare that "all the world's a stage" (from As You Like It) and "the play's the thing" (from Hamlet), as well as the name Sycorax from The Tempest. However, when Shakespeare himself coins the phrase "To be or not to be", the Doctor suggests he write it down, but Shakespeare considers it "too pretentious". In a different version of the joke, the Doctor exclaims "Once more unto the breach", and Shakespeare initially likes the phrase, before realizing it is one of his own from Henry V, which was probably written in early 1599.
The Comic Relief skit is another occasion of these two aspects of British culture intersecting, on a different TV show.