The phenomenon is not unique to Slovenia by any means. These shrines come in two types. The first one is the "znamenje" (sign), which is usually just a crucifix, or a small building with no space inside, with painted sides (or small statues). The second one is "kapelica" (small chapel) which has a small place inside, with a miniature altar.

Both types are indeed very common and usually stand next to roads, and especially at crossroads. Many of them were erected as a fulfilment of a promise or vow (I am not sure if this is a good English term), for example a soldier would build a small shrine if he returned safely from the war etc. Some of them are built in a place where you first see the church of the nearby village and are supposed to make a sign of the cross. A special kind is "kužno znamenje" (plague sign/monument) which were built as a thanks for the end of the big plague. They are usually in a form of a pillar and quite elaborately decorated.

Source: I am Slovenian