In addition to those mentioned by Jimi Jackson, I would add at least those three to the daily list because they're deemed important enough to be available for passengers in 1st class ICE trains throughout Germany (as well as Bild):

 - Die Welt: higher quality than Bild, but same publisher (Axel Springer SE).  Leans towards conservative/right
 - Handelsblatt: business / finance newspaper, contains several pages of nothing but commodity and stock exchange charts
 - Süddeutsche Zeitung: The name literally means South German newspaper and it's most prominent there, but it's also read in other regions. Leans towards center-left. Was involved in last year's publishing of the [Panama Papers][1], which perhaps justifies a comparison to The Guardian.

I'd also like to add that Der Spiegel is known for their investigative journalism. The most famous recent one was the involvement in publishing Edward Snowden's NSA documents.


  [1]: https://en.wikipedia.org/wiki/Panama_Papers