For those not familiar with how this works/worked: At most universities, a similar fee was collected from all students. That was then used to finance a regional "public transport flatrate".
N.b.: mk89 is technically not quite correct, it wasn't free (nothing in life is). It's usually bundled with the tuition/enrollment fee.
Implementation details differed per University, but for us the fee (80 or 100€, can't recall) was socialized across all students and payed together with the tuition fee; opting out was not possible (with some exceptions, like disabilities). The money went from the University administration to the AStA - the "general students council" (the executive section of the elected student self-government). The AStA then negotiated with the local public transport company/companies as well as with the Deutsche Bahn (e.g. to get access to certain inter-regional train connections - we still have cooperations with 3 or 4 nearby universities, and students somehow need to get there).
Those negotiations can be a royal pita, and often the students were in a weak position.
Source: I was in the AStA (~12 people), but not involved with that task.
So students basically never have to pay for the public transportation which is really awesome.
EDIT: by public transportation I mean whatever is included in the D-Ticket (no Intercity or similar types of trains).