I think it is safe to say we all know the Bella Ciao from Italy and also No pasarán from Spain is pretty well known, even if some don't really know or remind exactly where it comes from, they might have seen at some point something that relates to it.
In Spain, "No Pasarán" is a song but also a motto Spanish Republicans used in Madrid during the civil war as a way to boost the morale of the troops that were fighting the rebels who were also the fascists.
We also have "Ay Carmela", which doesn't originally come from the civil war but was also used during those times and nowadays it's more related to the civil war and their fight rather than for the original context which was the Napoleonic invasion of Spain in 1808.
"A las barricadas" is also pretty well known, it was sang by the anarchists side, who were also fighting alongside the Republicans against the fascists during the civil war. As far as I know, it's an adaptation from a Polish song from 1905, some maybe some Poles can give more information.
Els Segadors for Catalonia, which later on in 1991 also became their national anthem, is still sang to this day but not with such a meaning for the civil war as the original meaning behind is from a much older conflict.
Bandiera Rossa is also up there but not as known as it was more sang by the International Brigadiers. It's an Italian song so maybe some Italians can shed some light there.
Spain's civil war results are still present for many today, some lived through it and some that were taught by their parents or grandparents about it. Even today, Spain is still a 50/50 when it comes to their society. The woudns were not healed, they were just buried.