Which countries (in Mainland Europe or anywhere else around the world) currently allow you to purchase a ticket from any station in the country to any station in the country just like we offer here in the UK and Ireland? I know that this is one of the good things about our ticketing system and not all other countries offer this so i am just wondering in which other countries you can purchase a Single or Return ticket between any two stations in that country?
I think you need to clarify your question.
Firstly as mentioned by others, at least on Great Britain there are some station pairs between which it is not possible to purchase a ticket, because no fare is defined and/or it would not make sense to take a train between those stations.
If it does make sense to take a train, then surely it must be possible to buy some sort of ticket or possibly two or more tickets. As we know in Great Britain buying two tickets still comprises one journey but this may not be the case elsewhere - does your question refer to this?
Next, what sort of trains are we talking about? In Australia you can't buy a ticket from Liverpool to Sunbury because that would involve 3 different "systems" (Sydney Trains, NSW Trainlink, Metro Melbourne) but a similar journey in the UK might be Cockfosters to Ibrox, a journey for which one would not expect to buy a single ticket. Yet it is generally possible to do the equivalent in Germany (you can get a ticket from some random tram stop to a random bus stop in another city, involving several local services and an ICE).
Or are you referring to a country like Japan where there are several competing railways that run on broadly adjacent routes, and they don't sell tickets to stations outside their network?