Anyone who asks about "running out of" music, or written or spoken phrases, or computer programs, etc., need not worry.
It is physically possible to map out the simplest of all of these; most of them do nothing. Gibberish and such. A few extremely rare cases have relevance to us: meaning, feeling.
Anything with a length over a few hundred symbols will never be fully explored over the history of the universe.
Alternately, we can already say that all original media has been exhausted. Consider:
Write a '1' and a '0' on two separate sheets of paper. These will be our characters. (This is arguably the language of computers as we know them today, a perfectly valid starting point.)
Create an interpretation of these characters, a language. In that language, if you read '1', it translates to something; if you read '0', it translates to something else. What that "something" is, is unique to the particular language used.
There are infinite languages, therefore there are infinite interpretations of '1', and of '0'.
We don't even need two characters, really; this can be done in unary, where reading the one character gives the presence of a statement, and not reading it gives the absence of a statement.
Or we might make a very simple language, and express all statements through reading a sequence of '1's and '0's. We could even construct an infinite library organized by this system, mapping all original works, all translations, all covers and reinterpretations and critiques, and all gibberish, into a sequence of moves between buildings, floors, rooms, shelves and books. We would have the Library of Babel. I must warn you, though: it's a very boring place, where you'll wander your entire life having seen just a few complete words, never even a full sentence.
Such is the nature of large numbers, numbers of hundreds of digits. These are numbers large enough to be dense in prime numbers, and yet difficult to factor (relevant to modern cryptography); large enough to encode meaningful phrases, or musical phrases; or computer programs, even (or especially!) recursive programs (a program that creates programs, whether as a quine or as a self-referential "strange loop", if you will). We can encode mathematical proofs in these numbers, and we can equally well encode contradiction (Godel's Incompleteness Theorem).
Into the thousands, or millions of digits, we have quite complex numbers indeed, numbers that evolve -- genetic codes, codes that are also computer programs, which are running self-referential operations that will never resolve within our finite universe -- only propagate.
Tim