Is it possible to buy tickets for an international train in a third country in Europe?

I have tried this myself multiple times from my own country (Belgium) for different European countries (neighboring countries but also Italy, Austria, Czech Republic, Portugal, Switzerland ...)

In short, the only way to find out is trying. Some hints that might give you the best mileage:

• Forget vending machines. You won't get it there.
• Aim for main stations in major towns. It is possible that this shouldn't matter in theory, but in reality the person behind the counter will have a lot more experience with "weird" requests in a main station. Ideally you should go to a station where the have a separate counter for international travel.
• Focus on the main connections, especially the ones requiring reservations. Often you can buy those, even if it is impossible to buy tickets for regional trains. Buying the regional trains locally is usually not a big issue (unless you have a short connection time).
• Find an itinerary beforehand (I prefer the site of the DB), print it and show it. The train number can be a pointer and at least it shows the person behind the counter that she/he is looking for something that exists and not going on a wild goose chase.
• Try it during busy office hours. The more people hanging around, the higher the chance that one of them is an experienced colleague that tried it before and knows how to get it out of the computer. Or that knows it is impossible.
• Bring your thickest skin possible. You might be occupying the counter for a while. People queuing behind you might be getting nervous.
• Stay friendly and be prepared to take "Computer says 'no'" as an answer.

In the old days (say 15 years ago) you could buy more or less tickets between any arbitrary two stations. Now with privatizations and strict EU regulations on competition, the number of rail operators has exploded and the situation changes rapidly. What was possible last month, might not be possible today and the other way around. The people behind the counter often have to try themselves.

To summarize and nuance the earlier answers, I know from experience that it's possible to buy tickets in or between third countries at train stations in Europe but it's often a frustrating experience. Some trains might not be available or it might be possible to get a ticket but not to book a seat. Sometimes it even depends on who you happen to ask, some railway employees seem more adept than others at finding and booking complex tickets abroad.

Also note than in some countries, booking an international ticket might require you to go to a special service desk and to pay an additional booking fee or at least to find a manned ticket office. For example in the Netherlands, many stations don't have a ticket office anymore, medium ones do but won't sell tickets outside of the Benelux and Germany and there are only a handful of NS International desks (the new brand for NS Hispeed) in places like Rotterdam and Amsterdam.

Whether a ticket that's not available on the web is more or less likely to be bookable at the station I don't know. I think they do use several different systems and if you find the right person, you might still have a chance to buy a ticket. The annoying thing is that a clerk who doesn't know the system very well will often be adamant that a train does not exist or is not bookable even if there was in fact a solution.

Finally, travel agents might be able to help as well (or not).

Yes you can, although in some cases it might be bit complicated. I checked the website of the Dutch railways where I noticed the following announcement:

Online, NS International sells a wide range of both trips departing from the Netherlands to other countries (one-way and return) and coming from abroad to the Netherlands (one-way and return), as well as a limited number of routes from abroad to another foreign country (one-way and return). Other trips can be booked by telephone via Service Center (0900-9296,) and at desks at Tickets & Service offices at all medium to large train stations.

So at least in the Netherlands you should be able to buy your traintickets at the international desks at certain stations. I expect this to be similar in other countires as well.

Yes you can.

Inside of Europe

Local European train stations offer you the possibility to buy international tickets from and to where ever you want in Europe through either their website or their local ticket shops.

Outside of Europe

I'm not sure if they do, but if they don't, you could always ask them to go the European international railway website and ask them to buy the ticket online for you.

Website to buy international European tickets