OK, I promised I would come back to this. First of all, I don't know what kind of music style you'd like to listen to, my favourite is rock, so that will be most of my recommendations.
I think if you're looking for some Spanish legends, Joan Manuel Serrat and Camarón de la Isla are the best place to begin with, since I heard of them in school. Rolling Stone Spain chose Serrat's
Mediterraneo as the greatest Spanish song ever, and I think he sings his lyrics quite clearly, so it's a definitive first-listen choice. However, if Camarón, the king of flamenco, is clearly a must-listen too, the way flamenco singers sing is such that trying to decipher their lyrics is not the best way to begin, I believe. Nevertheless, you should really listen to him at one point or another (the album
La leyenda del tiempo contains some of his most well-known songs, like the title song or
Volando voy. If you like flamenco, the song
Omega by Enrique Morente & Lagartija Nick is probably the best song I've ever listened to in the style so far.
Regarding straightforward rock music, I think the greatest Spanish-speaking rock band of all times is from Argentine, and is called Soda Stereo. I love the voice and the way of singing of their leader Gustavo Cerati, the only point that could be a drawback is the fact that most of his lyrics are surreal, and that the accent of Argentinian is slightly different from that of native Spanish people. If you choose to still go ahead and listen to them, there's a lot of places to stop. I've made a topic about them once, here:
viewtopic.php?f=2&t=1359
My favourite Spanish-speaking rock artists past them are Andrés Calamaro (Argentina) and Los Prisioneros (Chile). Radio Futura (Spain) are also a great band that I like. In the arena rock department, I would also recommend Los Héroes del Silencio (Spain), but I'm not a fan of them, not yet at least.
Regarding pop, I love a Spanish band called Mecano, however, I know it's not everyone's cup of tea. Their ballads, like
Cruz de navajas,
Hijo de la luna or
Mujer contra mujer are their most well-known works.
If you're more into folk (I'm trying to cover as much genres as possible), I've mostly listened to Chilean protest folk singers, most of them are legends in Chile: Violetta Parra, Víctor Jara are the most important. I believe Chilean uses some vocabulary that is different from academic Spanish, so that's why I would still be careful.
In the hip-hop department, Tiro de Gracia and Illya Kuryaki & the Valderramas are the only ones I've listened to so far. The former authored
Ser humano!!, one of the greatest hip-hop albums I've ever listened to.
As for one-hit wonders, I would recommend Jeanette's
Porque te vas (pop), Extremoduro's
So Payaso (hard rock), Alarma's
Frio (new wave), they are the ones that come from the top of my head.
I guess Blanco shall be a better teacher than me, I would love to see his own recommendations