Sources for the Prohibition of Listening to Music

There are a number of sources for the prohibition of listening to music nowadays:*

Mishna Sotah 9:11

From the time that the Sanhedrin ceased to function, there ceased to be music [alt : song] at beit haMishtaot.

Gittin 7a

Mar Ukva was asked whence we know that singing is prohibited.
He answered: because of the verse in Hosea [9 :1]: "Do not rejoice,
o Israel, as the other nations rejoice."

Rambam Hilchot Taanis 5 :14

So too [that is, besides various other decrees] they [the
Rabbis at the time of the destruction of the Second
Temple] decreed that no one play upon musical
instruments; moreover, it is forbidden to rejoice with,
or listen to, all kinds of music and all that produce the
sound of music - and even singing of voice alone,
over wine, is forbidden as it is written: "with song
they shall not drink wine" [Isaiah 24:9]. It has
already become customary for all of Israel to say
words of praise or songs of thanksgiving to G-d, and
similar songs, over wine.

Orach Chayim 560:3

So too they decreed against the playing of musical
instruments and all forms of music and all that
produce sound of music to rejoice with. Moreover, it
is forbidden to listen to them. All this is on account of
the destruction of the Temple.

Rema: There are some opinions that the prohibition against
musical instruments is only for those who listen with
regularity such as the kings who arise and go to bed
with musical instruments, or for musical instruments
at parties and feasts [that is, where there is drinking].

And even songs [vocal music] with wine is forbidden
as it is written "With song they shall not drink wine"
[Isaiah 24 :9]. It has already become the custom of all
Israel to utter, over wine, words of praise or songs of
thanksgiving and commemorations of G-d's
kindnesses.

Rema: And so too for the purpose of a mitzvah, such as in
the house of a groom and bride, it is all permissible.

There is much recent discussion in the poskim about how the prohibition works nowadays. Here is a list of some sources:

Iggros Moshe O.C. 1:166
Yechaveh Daas 1:45
Az Nidberu 8:58
Tzitz Eliezer 15:33
Seridei Aish 2:12

*For further discussion on this topic see Rabbi Aharon Kahn's Music in Halachic Perspective in Volume 14 of The Journal of Halacha and Contemporary Society. And, of course, for final rulings consult your local competent halachic authority.