I guess you should listen something serious, not a junk pop-music, for example. As for me, I really like listen Sting songs because of their different compound words. It helps me for learning English.

I think that we have the same Sting, who has very interesting serious texts - it is Alexander Rosenbaum. 

You may listen, for example:

Александр Розенбаум & Григорий Лепс - Последний рейс

Александр Розенбаум - Колыбельная (I really love it)

Александр Розенбаум - Дай мне минуту (It is very strong) 

You may also like such singers as Александр Градский ("Как молоды мы были", "Вот так папа пел"), Олег Митяев ("Мама"), Булат Окуджава. Try to listen Константин Никольский "Музыкант". 

There is many Russian songs which can help you with learning. It depends what you prefer :) 

Regards! 

Russian films and serials are better for studying Russian I guess

Лучшие детские песни http://www.youtube.com/watch?v=3yjIE_Az2N4

I think that from alternative rock you can find some interesting groups such as the Pilot (Пилот), Animal Jazz, Lumen etc. All of them have great songs. Good luck.

Ленинград — Рыба / Leningrad — Fish

https://www.youtube.com/watch?v=a-CnWwbeetE