Answer:
There are several countries without trains or railways. Most are either small countries on islands (Iceland for example, has none) or poor countries that really can't afford the cost of maintaining them. HOWEVER most of these countries HAVE HAD railways of some kind at one time or another (Guyana, for example has pretty much nothing but was in fact the first country in South America to have railways at all. Iceland also has had a few small railways built temporarily in the past for construction purposes).
As an aside, it is not always necessarily the countries fault that they have no railways. Many are former colonies of European countries that all had outside influence on the railway construction. Sometimes, if more than one power had a grip on an area, railways of completely different gauges (sizes) would be built by the opposing powers.
Also, the countries obviously only cared about the railways (and the colonies themselves) as a means to make THEM stronger, so the railway systems usually only consisted of a line going straight from whatever rare mineral or something that they wanted to the nearest port, for shipment back to the main country.
Not only were these impractical for serving the entire nation, they were (and still kinda are) a symbol of their former tyrants to the locals. So when the little countries finally broke away from their oppressors they often wanted little to do with railways or trains.
As far as lists of all the countries that don't have them, they aren't really complete, although train buffs like these guys will throw out some names and see if they've got trains or not.
Explanation:
