Mark Forster sings in German (pop songs), I especially like his older songs (Au revoir, Flash mich).
Peter Fox´s music is something different, but cool. (E.g. Haus am See, das zweite Gesicht)
Silbermond is a great group, I love Weiße Fahnen from them.
Then there´s German rap, of course, and although I can´t stand the rap songs in the German charts, there are some good rappers, when I was a little bit younger I used to listen to Sido. Especially if you wanna learn vulgar language 0.0. He has more mellow songs, too. (Herz, der Himmel soll warten, ...)
Some while ago we had LEA´s 'Leiser' in the charts, it´s a nice, soft song.
I´m a huge fan of Alligatoah, but his music is veeery special and you should be an advanced German learner so you´re able to understand the satire.
Plus, if you´re into that, there might be German versions of English songs. Disney would be a prime example (although lots of people complain they´re awful in German), but also regular musical. I´m pretty sure there´s a German version of Wicked somewhere on YouTube.
There are the first few that come to my mind, of course there are millions of other artists who´re amazing musicians! Have fun discovering them! :-)