Since the 2nd April there is a new feature on the DB website which allows you to cancel your tickets without having to call or go to a ticket counter. You just need the ticket code and name of the passenger:

https://fahrkarten.bahn.de/privatkun...e&lang=de#stay

In my case, I had bought two tickets for somebody else who will not need to go to that particular destination again at any time in the future. I managed to cancel the ticket instantly and received the code for a voucher equivalent to the original price of the ticket. I think I will be able to use the code for a ticket in my name in the future, I don't see any reason why this would not be the case. I am happy to accept a voucher from Deutsche Bahn, because it is certain that they will be here in the future, unlike many of the airlines.

A couple of relevant data points:
- The ticket I cancelled had already taken place about a week ago;
- The voucher is valid for 3 years, which is really good.