[Xylakant]

Your petition might get a reading in the Parliament and you're allowed to speak. However, this is not a guaranteed outcome, the Bundestag or rather the committee in charge of petitions may deny you the public reading with a 2/3 majority.

However, on the state level there is a "Volksentscheid" where the people can directly vote or enforce a vote on an issue. The quorum and the topics that are eligible for a Volksentscheid depend on the states legislation. Berlin for example allows a vote on general topics of interest while other states only allow votes on proposed laws.

[tobinfricke]

Have there been any particularly notable uses or outcomes of this process?

[Xylakant]

The most notable outcome was probably the petition against internet blocks in germany [1] which was signed by more than 130 000 persons and was a crucial milestone in gathering public attention which ultimately brought the law to a fall.

[1] you know, against child porn. See http://en.wikipedia.org/wiki/Zugangserschwerungsgesetz for a short summary.