If I have purchased a ticket on DB for a specific train, am I allowed to board at a stop between the origin and destination printed on my ticket? Specifically, if I have a ticket from Frankfurt main station to Düsseldorf, can I board at Frankfurt Airport, which is the stop immediately after Frankfurt Main?
Yes you can as they don't check tickets that early in the ride.
Ten (or more?) years ago, there was a low-cost airline (American SW?) flying directly from Colorado Springs to cities in the eastern US. They had really good prices. United matched their prices from Co. Springs, but not from Denver, but the United flight from Co. Springs had a change of planes in Denver. People would book the cheaper flight with American SW, go to Co. Springs to board the flight to the eastern city and fly through Denver, but, on the way back, get off the plane in Denver (where they lived).
Well, United found out about this and was going to charge people more money for not flying United to Co. Springs. I don't remember what happened, but I think United thought better about it and didn't try to charge them. (Hey, I didn't fly United to Co. Springs today, or yesterday, so you owe me money.)
But the Bahn is not like an airline. They charge you for the distance you travel on the train. Their tickets are not more because that route is more popular. They're not going to charge you for getting off early or getting on late.
I don't think the conductor will care if he didn't see your ticket when you were between the Hbf and the airport (he might not even have been checking tickets in your car during those 11 minutes.) He will only be concerned that you have tickets covering the parts of the route you actually take.
To board at a later station is fine, as is getting off at an earlier station. All they care is that your ticket is good for the route and train you are on.
Only using part of your ticket is perfectly legal. So boarding at a later station, get of at an earlier station is all fine, and even if the conductor finds out what you are doing (eg. he sees you boarding at the Airport) you will not be in trouble.
Trains work on the "Proof of Purchase" principle. In order to be rightfully on board a train you need to be able to show something that says that you have paid for that train (or the route the train is on). There are no other requirements really.
With reservations the situation is a bit different. Reservations lapse after 15 minutes. You will see that they disappear on the electronic displays. So if you do not occupy your seat within 15 minutes after the train has left the station where the reservation starts then you lose it.
As long as you finally board the train number which you bought the ticket for - it is allowed.
Generally I second the statement about the seat reservation from WengenK. I am not sure if they delete the "Frankfurt - Düsseldorf" already after leaving Frankfurt Hbf or if they see FRA airport as last Frankfurt.
I did what you described a couple years ago. I purchased a ticket in advance from a city in Germany from DB Bahn that ended in Italy and actually started our trip in Zurich. Unlike air travel, its legal to do this.
As for seat reservations, the practical standard is if someone is in your seats, and you show them your reservation, they will move, happens all the time from my observations. Of course if they are clueless tourists, you may need to explain, but generally everyone I have seen respects the reservation
Thanks to everyone for the helpful replies confirming what I hoped to be true. I know that airlines can be jerks about passengers boarding or deplaning at stops other than their ticketed pair, and assumed that trains were different. In the U.S. it's not a problem. For example, if I buy an Amtrak ticket from Portland to Seattle, I can board in Vancouver WA, across the river from Portland. But I wanted to be sure about the situation in Deutschland.