Joel and Ethan Coen have famously said that neither of them has ever read Homer's Odyssey, and implied that the credits to their film O Brother Where Art Thou?, which say that their screenplay is "based on Homer's Odyssey," should be taken with a chuckle. And yet, even if the credits had not mentioned Homer, anyone with a passing familiarity with the plot of the Odyssey could've seen the big obvious parallels, from the protagonist being named Ulysses, to the many adventures suffered by Ulysses and his companions on their way home, to the characters clearly based on the Sirens and the Cyclops, to Ulysses' having to to defeat a suitor to win back his bride once he's home, to name but a few.
Some might see it as a sign of the collapse of Western civilization that Joel and Ethan Coen, two of the most well-respected artists in contemporary culture, have not read Homer -- but look at it another way: Homer is still so much a part of our culture that they didn't need to read the Odyssey in order to make a great film based upon it.
In 1997 Charles Frazier published his first novel, Cold Mountain, the story of a man who deserts the Confederate Army near the end of the American Civil War and embarks on a long and hazardous journey to return to the love of his life -- a novel based on the Odyssey, and perhaps the best-reviewed American novel of the past 25 years. Since then, many books based on the Odyssey have been published, notably Margaret Atwood's novel The Penelopiad, which re-tells the story from the point of view of Odysseus' Penelope. In 1922 James Joyce published Ulysses, one of the most highly-regarded novels of the 20th century, and one very self-consciously and minutely following the plot of the Odyssey.
And those are just a few of the most prominent imitations of the poem. Just to name every well-received novel, poem, film, play, ballet and other work of art made in the 20th or 21st century based on the Odyssey would fill up a longish blog post, even if I stuck to just the US, Canada, the UK, Ireland, Germany, Austria and Switzerland, whose 20th- and 21st-century culture I happen to know somewhat better than that of the rest of the world. I'm not well-acquainted with the literature of the Caribbean, but I do know that the Nobel Laureate Derek Walcott, of Saint Lucia, wrote a book-length poem, Omeros, which is based on the Iliad.
Looking at the cream of recent Western culture, it would seem that the continuity of the Classical tradition is mightily strong indeed. (And by the way: in the abundance of re-tellings of Homer, recent Western civilization resembles every single earlier epoch.) But some might say that it has declined drastically, and point to academia, always closely related to ambitious fiction and poetry, but never identical to them, to make that case. But I am not so sure. It's a matter of how you look.
Up until about a century ago, Western academia was with very few exceptions the preserve of affluent white men, a fairly small club which saw itself as the inheritors and preservers of, among other things, ancient Greek and Latin literature. Since then, much greater numbers of people have been going to college, primarily from groups which had been mostly excluded from it before: women, ethnic minorities and people who aren't quite so rich. Understandably, not everyone in these groups new to academia shares all of the same opinions about what is important as the traditional core of rich white guys. Some lament a decline of the study of the Classics, and compared to academia as a whole, there's no doubt that Classics have a smaller place than they had a century ago. But in terms of the actual numbers of people studying ancient Greek and Latin, writing books about it, teaching it to others and editing Classical texts -- well, there, I don't know how the actual total numbers today compared to those of a century ago, and I don't know whether anyone else knows either. If you know, please tell me! If you think you know, well, don't feel compelled to share your opinions. I have my opinions and am familiar with those of some other people. What I don't have are actual numbers.
It may well be that there is one huge advantage enjoyed by Classical Studies today compared to a century ago: it may be that the general level of enthusiasm in Classical departments is much higher today -- when no study of the Classics is required in most universities, meaning that the Classics departments are filled with students who have chosen to be there -- than a century ago, when a certain amount of Classical study was required of every single rich white guy, in college and before college, and to many of them, perhaps most, the Classics were a loathsome chore, to be endured and then, if possible, forgotten.