The first thing the words "Spanish music" probably make you think of is flamenco, while the second is very likely to be Iglesias (père or fils). Fortunately, while music has rarely had the same prestige as art in Spanish culture, both its musical heritage and its current music scene are naturally much richer than that, Spain's unique history and variety of cultures combining to make a mosaic of sounds, though usually with a certain Spanish feel to them, a hint of something significantly removed from the European mainstream.

So far, the themes Spain and Portugal for Visitors covers under the heading "Spanish Music" are these:
Spanish Classical Music (using the word "classical" in its loosest sense)
Fado, sometimes called "the Portuguese blues"
Flamenco, Spain's most emblematic music form.
Spanish Folk, a fascinating, dense subject because of Spain's striking regional differences, and
Spanish Pop and Rock, sometimes excellent, sometimes not so good, but almost never as bad as some snidey rock critics would have you believe.

A bit self-indulgently (as a sometime guitarist), I've started adding content for those who might be interested in picking up a real Spanish guitar while they are visiting, as well, whether classical or flamenco:
Madrid Luthiers, many of the finest (and most expensive) guitar makers in Spain being based in Madrid.