First, it is very, very unlikely for German ICEs to have all seats reserved. Many Germans don’t reserve their seats because they either have season tickets or a non-fixed itinerary or don’t want to pay the reservation fee. (This may change once reservations are included in the ticket price, but that has recently been postponed to a later, unannounced date.)
However, it still happens that a train is full of people despite not being fully reserved. Often, this is because a double unit of one of the later ICE builds (not the first generation; they are a single train not designed for doubling or splitting) is reduced to a single unit (typically due to technical problems). In much rarer cases this is due to a demand higher than what can be accomodated (Hamburg–Copenhagen was one before they introduced compulsory reservation a few years ago). If this happens, there is a number of things that can happen:
The train still leaves because the staff decides it is safe.
This will typically be the case if there are people standing in the corridors, but it is not fully packed and people can still walk back and forth.
- Occasionally, the first class is opened to second class passangers (more likely on regional trains, though, where the price difference is less).
The train won’t leave because staff decides it is no longer considered safe.
People are then asked to leave nicely, then less nicely. (Contrary to the other answer, I have never heard of the offer of vouchers to voluntarily leaving.)
The police is called and forcefully removes random people from the train.
Once enough people have removed themselves/have been removed, the train leaves with often considerable delay.
To reduce your odds of falling victim to the second bullet point, it is helpful to be among the first to board a train, even if that involves an odd bit of pushing and shoving (seen as highly unfriendly, of course; don’t overdo it!). Typically, those closest to the exits will be removed if the police are called.
Also, when grabbing any empty seat, make note whether the little electronic sign above it notes two stations between which the seat is reserved. Occasionally, it says ggf. freigeben instead, because somebody booked the reservation only shortly before departure, or it says bahn.comfort for a special contingent of seats offered to the frequent travellers who acquired comfort status. If your seat says neither, it is extremely unlikely that you are removed from the train. The police does not check tickets to remove any passanger preferentially.
Finally, the Zürich–Hamburg train is one that is not too likely to be full — however, the peak travel times are Friday afternoons and Sundays. During those days you may have a harder time finding a seat. I haven’t had a train of that particular relation being too full to leave yet, though; and it is typically served by the oldest ICE generation.
: I used to think that ggf. freigeben could also mean the train’s IT failed. Turns out that in that case the signs would read GGF. FREIGEBEN in capital letters, making it easy to distinguish the two. When I saw the all caps version (displayed on every seat, so obviously erroneous), I attributed it to a different ICE build than what I normally travel with.