Judging newspapers on their political affiliation may be highly subjective, but I'll just give my thoughts on those I have experience with.
Bild: Germany's leading tabloid. Similar to Britain's Sun, but more moderate in comparison. Has been staunchly conservative in the past, but I can't make out a certain political affiliation today. Being a tabloid, it does have a tendency towards populist simplification and sensationalist misinformation though. Trademark style is very short sentences that "everyone can understand".
Frankfurter Allgemeine Zeitung (FAZ): probably Germany's most reputable daily newspaper. Leans centre-right, but it does a good enough job of keeping news and commentary separate to be respected even by political opponents. Fairly intellectually demanding by newspapers standards.
Frankfurter Rundschau (FR): Was once the centre-left alternative to the FAZ, but has suffered severe economic trouble and is sadly only a shadow of its former self.
Die Tageszeitung (Taz): very left-leaning, shunned by some for its political tendencies, but still somewhat respected not only in the left camp.
Der Spiegel: Germany's leading weekly magazine, similar to America's Time Magazine. It is controversial, often polarising, somewhat leans left but without catering to leftist parties. No matter your political preferences, Der Spiegel is highly influential, one of the most important opinion-forming publications in Germany.
Stern: another weekly magazine but lighter on content and heavier on images, clearly less important than Der Spiegel.
Focus: The third of Germany's big three weekly magazines. Has a mixed reputation, certainly below that of Der Spiegel. Affiliation is centre-right.
Die ZEIT: Weekly newspaper that mostly consists of opinion pieces, is mostly well respected and has a reputation of providing intellectual debate. While it gives anyone a voice who isn't extremist, I have a feeling it leans centre-left.