As Frank says, it depends on the kind of ticket you have. Standard, full fare ticket it will be usable on any train of the same type and for the same route for some time (a month?) At least that is how it works in Germany. If it's an advance purchase, discounted, train specific ticket, and it's their fault you miss the train, you will have to get it endorsed at a ticket counter to use it.
In 2008, I had a Sparpreis ticket from a regional station in Niedersachsen, connecting to an IC to Karlsruhe. The regional train was late arriving at the connecting station, so I went to the counter. The agent looked at my ticket, checked his computer to make sure the connecting train truly was late, then wrote down the number for the following train, an ICE.
Last year I flew into FRA and took trains to the Black Forest. Due to uncertainty about trans-Atlantic arrivals, I bought a full fare ticket. I thought if I arrived on time or a little early, I might make a certain train, one leaving shortly after my scheduled arrival. I bought the ticket for that train in advance, because I knew if I could make that train, time would be tight, and I wouldn't want to take time buying the ticket. As it was, the plane was a little late. I was able to use the ticket, without any endorsement, for the next connection.