This question occurred to me after chancing across some miscellaneous information. By "largest countries", I mean in economic terms rather than geographic size. In some cases the railways have fallen into general disrepair or neglect, or have lost the traffic they were originally built for. In other cases marginal railways are not repaired after damage from storms or earthquakes.
For example, the railways of Costa Rica have been mostly inoperative following an earthquake in 1995. As of 2013, there are some commuter trains out of San Jose.
The railways of Ecuador are mostly inoperative except for limited operation of tourist trains. Similar situation in Paraguay, but now even the limited tourist train operations have been discontinued.
Afghanistan has never had any significant rail system. There used to be a tramway in Kabul? There are maybe a couple border towns where rails come in from the next country.
I don't have a lot of internet time to research this topic, but maybe others will contribute with what they know or find out.