There are a number of ride-sharing services, the self-proclaimed biggest being blablacar.de, previously known as mitfahrgelegenheiten.de, I believe.
We also have a multitude of car-sharing services, where if you subscribe, you can look for a free car parked somewhere, and then drive it wherever you want within a certain area. Examples are car2go, DriveNow, and I believe Starcar and other rental-car companies also have services like that.
Uber actually had to pull out of several german cities because of taxi-related regulations. Taxi-drivers in those cities need to obtain a license, which drivers for Uber obviously don't do. So (some german) institutions also view Uber as a taxi company.
Source: https://www.theverge.com/2015/10/30/9648676/uber-germany-ham...
Why is something like Uber called ride-sharing to begin with? I'm not sharing my ride with anyone that coincidentally wants to travel (more or less) the same route as me. I pay somebody to drive their car first to me, and then some other place.
This is called a taxi or cab [1], there Uber is a taxi company.
At least in Germany, there used to be actual ride-sharing systems, of which the best one used to be mitfahrzentrale.de, where people would advertise what route they were planing to drive (and when) and other people could "book" a seat on that route. I don't know if some others still exist, I haven't used them in years.
[1] https://en.wikipedia.org/wiki/Taxicab