These two bands are what I would call Alternative Rock, and they hail from Germany! I learned of both bands from the previously mentioned IMF, and the first band, Madsen, is the band I personally prefer because of the fact that I've listened to and enjoyed more of their songs. However, both of the following songs, I really really enjoy.
Madsen- Du schreibst Geschichte (You write stories)
Another great song by Madsen to check out if your interested is Goodbye Logik, which is also quite good. It's got a great beat that gets you moving.
Killerpilze- Springt hoch (Jump high)
Killerpilze is a young band, and they've got a few other good songs. They have a sort of skater alternative sound, to me at least, and that's not exactly my favorite kind of music, so I don't enjoy it as much as Madsen. However, if you enjoy that kind of music, and Killerpilze appeals to you, definitely find more on Youtube. There is plenty there!
I hope you enjoyed these German bands, and got a taste of what the German language can do for music. I think it adds a wonderful dimension to it that proves that German is not the ugly language so many people label it to be.