On this site you can search for lyrics of different musicians. Often the lyrics page has a video of the song as well!
http://lyrics.wikia.com/Валерий_Меладзе_(Valerii_Meladze):Сэра
The following is a karaoke site, where you also can search for specific songs/musicians.
It plays the music without the sung lyrics but with written prompts when to sing the lyrics.
Here another site of international lyrics with a choice of translations into several languages (I don’t know how good the translations are as my Russian isn’t good enough yet, but the French or English to German translations I checked were quite good!)
Hi ! =)))
I read an English translation! =))) Yes, you are right! =)))
I only have to pay your attention to the specifics of the poetry and song lyrics sentence structure! =))) Please, keep in mind, for the sake of the rhyme the word order in the sentences is nearly always a bit unnatural, that’s exactly why it’s sometimes called ‘poetic sentence structure’ normally implying that the word order may either be an inverted one, or just absolutely special! 
Again, it only matters from the viewpoint of using these lyrics as language learning material, and if necessary, I can amend those lines, where the word order just does not coincide with that of the source lines!
They are not numerous, by the way!
Here is a playlist of pop music videos with text.
Thanks a lot for that play list angiemc - there are a few nice songs and the in-video lyrics are great!
Anybody knows of similar play lists, please post them!