Can you identify a work that reflects or alludes to Shakespeare and explain how this allusion is used thematically?

If you're still looking for ideas, I might suggest a quick look at famous Shakespeare lines which have insinuated themselves into everyday language and usage, such as "The lady doth protest too much, methinks" and "catch my drift." One of the Star Trek movies is titled from a line in one of Hamlet's soliloquys--The Undiscovered Country. More titles and phrases come from Shakespeare than most people imagine.

As others have noted, there are many modern films which are loose versions of Shakespeare's plays. The film O with Josh Hartnett is Shakespeare's Othello; similarly, 10 Things I Hate about You is a version of the bard's Taming of the Shrew. The older musical Kiss Me Kate (which was revised a couple of years ago) is also a "remake" of Taming of the Shrew.

In regards to simple Shakespearean allusions, we often use the phrase "green-eyed monster" when referring to envy or jealousy--it comes from Othello. Likewise, "a rose by any other name" appears in many works and comes from Romeo and Juliet. A specific example of a take on the "rose" allusion is the title of a chapter from the bestselling book Freakonomics. The chapter is entitled, "A Roshanda by Any Other Name. . ." and discusses whether names bear any significance on someone's success.

An example of a whole work of literature based on Hamlet is Rosencrantz and Guildenstern are Dead by Tom Stoppard.  The play is a great example of the existential ideas of the mid-20th century and a take off on the theatre of the absurd. 

A fictionalized story of Shakespeare's life and writing of Romeo and Juliet is the movie Shakespeare in Love.  The more you know of the specifics of not just the language of R and J but all of the Shakespeare's plays, the more fun the movie is -- the screenwriters (Tom Stoppard most notably) slipped in all kinds of famous lines from several plays into the text of this movie script.

The most recent example I can suggest is the newly released Gnomeo and Juliet. It is a loose re-telling of the story, but it is about two households of garden gnomes.  Again, the better you know the original, the better the movie is.

I'll give you an two examples, one modern and popular, one older and more classic.

The older one is the book Brave New World.  That book is full of Shakespeare references as allusions (the title is one) because the author is using Shakespeare as a symbol of humanity and human emotions.  The author quotes from Hamlet, for example, to show the hatred that John feels for his mother because of what he sees as her sexual immorality.

The new one is Taylor Swift's song "Love Story."  The calls herself "Juliet" and her love "Romeo" as a way to refer to the idea that her parents did not want the two of them together at first.

From your question, it wasn't clear how long the assignment is or what constitutes a "work."  I hope one of these might be useful.

I don't know if you are permitted to use a movie as a "text," but The Lion King is certainly based loosely on Hamlet, and there are even allusions to Shakespeare in the movie.  There is an wicked uncle who kills the father and tries to take over the kingdom, and a son who is left to deal with this.  The endings are quite different, but there are enough similarities to fit the bill. 

Westside Story also comes to mind, as a modern treatment of Romeo and Juliet.  The lovers in the movie are representative of Romeo and Juliet and the houses of Montague and Capulet.

For a real "text, there is Jane Smile's novel, A Thousand Acres, which is based to some degree on King Lear. It is a very good novel, too, I might add. 

As you explore the themes of these three Shakespeare plays on enotes, you will be able to make good thematic connections between these works and the plays. 

I must say that as I get older, I notice fewer and fewer allusions to Shakespeare among younger people, and I think that is a shame.  He is one of our richest sources of expression in the English language, and as you read more and more of his plays, you will be able to find lines that you have heard before.  You can use them for yourself, and make sure that the beauty and richness of his plays is not lost.  This is a good assignment. 

Which work alludes to Shakespeare and how does the author use this thematically?

Check out Jane Smiley's A Thousand Acres, which is a fantastic retelling of King Lear.  It's set in modern times, with a farmer who divides his land among his three daughters, but it's complicated by a history of family abuse.  In King Lear, it's unclear why Lear's daughters Regan and Goneril are so cruel to their father and only the youngest, Cordelia, is kind to him, and the audience is left to assume that there is something inherently wrong with G & R.  In A Thousand Acres, however, Smiley adds a history of family abuse.  The older sisters in Smiley's book were abused by their father, so they have a real conflict with their father, and a legitimate reason for being unkind.  The youngest daughter, on the other hand, was not abused, and she has a much easier relationship with their dad--and like Cordelia, can't understand why her sisters are so unloving.

James Joyce's Ulysses has countless allusions to Shakespeare.  (They are listed, by play, in Weldon Thornton's Allusions in Ulysses.)

Hamlet's Dresser, by Bob Smith, is an autobiography that tells of the author's lonely and sad childhood and recalls the way in which Shakespeare's works changed his life. 

Gertrude and Claudius is a novel by John Updike that examines the story of Hamlet from a different perspective (focusing on the relationship of the title pair). 

O is a 2001 film whose story parallels Shakespeare's Othello.  The language and situations are modern, but the story is almost identical.

The first thing I thought of when I saw your question was, of course...Star Trek VI:  The Undiscovered Country.  This line comes from Hamlet's "To be" soliloquy. in which he is pondering whether to live or to die.  He asks, who would bear all the grief and burdens,

Death is the beginning of eternity, life after death--the undiscovered country--the place no one knows enough about to risk suicide and the damnation that might bring.

Movies quote Shakespeare lines or make references to his work all the time.  Music does the same--lots of Romeo and Juliet references.

One other place which is always making literary allusions is Gilmore Girls, though I can't think of a specific Shakespeare reference offhand. 

One novel that uses a Shakespearean allusion both titularly and thematically is Aldous Huxley's Brave New World. The title comes from The Tempest, and in the play, it's meant to be taken at face value, praising the new world "that has such people in't." Yet in Brave New World, John the Savage uses the reference ironically. He's been dragged into a world that is full of madness and immorality in his eyes. For him, it becomes almost a hell on earth. There's several othe Shakespearean allusions in the novel as well. John reads to Helmholtz from Romeo and Juliet (at which he laughs, unable to understand the emotions between the young lovers). He also imagines himself Othello, seeing Lenina as a betraying Desdemona.

The West Side Story is a musical written to mirror Romeo and Juliet.

Ten Things I Hate About You is a modern-day satire to Shakespeare's classic Taming of the Shrew.

Many authors have used Shakespeare's words in their titles. William Faulkner used The Sound and the Fury. Agatha Christie used By the Pricking of My Thumbs, and Ray Bradbury used Something Wicked this way Comes.

But perhaps a really good work for you to research is "The Lovesong of J. Alfred Prufrock" (1917) by T.S. Eliot. He alludes to a Prince Hamlet character for his main character. This shows the main character struggling with a difficulty and realizing he cannot struggle through a situation as well as the character Hamlet in Shakespeare's play Hamlet.

How to Read Literature Like a Professor is a book worth checking out that has many of these allusions.