I can't really find a conclusive answer other than that they are left over from a time when these small 'countries' where the norm. But all those other ones faded away, except these. Why is that? Is it just too much trouble for such a small space of land and France, Germany and Italy just never bothered?
A quality post on Liechtenstein from 5 days ago by u/jasperdegrote and u/robbyslaughter
https://www.reddit.com/r/AskHistorians/comments/5ktur6/why_is_liechtenstein/
I wrote about the history of San Marino here. In short, the territorial expansion of the Papacy in the twelfth century involved the absorption of hodgepodge of independent cities, multi-level feudal holdings, cities within feudal holdings, and cities run by citizens with feudal holdings. In short, thousands of San Marinos of varying size and power.
Over the next century, Papal policy would center on consolidating control over these lands, be it through legal scheming, opportunism, or even force of arms. In the late 13th century, the Papal legate in Fermo was by some machinations able to appoint a Rector in Ancona. San Marino, a small Republican community in the foothills of the Apennines at the time little different from many other communes in north-central Italy, conveniently produced an "ancient" document attesting to the town's ancient independence when the local Abbot came to claim the church's shares of taxes. San Marino was able to keep the local Papal legate out of local affairs.
To small to really bother anyone, San Marino continued governing itself like many other Italian cities, but it's unclear how "independent" a polity like San Marino could be in the early modern era; for example as the Papacy extended it's power over Sigsmondo Malatesta's domain in the 15th century, San Marino "sided" with the Papacy against their neighbor. In return, the tiny republic was granted an expanded territory. San Marino was unceremoniously included in Cesare Borgia's Vassal state in Romagna, and in the 1700's Papal representatives tried (and nearly succeeded) in dismantling the republican institutions. However, at the end of each failed occupation the Republic's government affirmed more and more sovereign powers, such that by the time Napoleon rolled along, he finally put the issue to rest and affirmed his admiration for the "Model Democracy".
I also wrote about Monaco here. Monaco was the a possession of the Genoese Grimaldi Family, who were subsequently affiliated with Spain, the Piedmontese, and finally France. During the French Revolution, the Grimaldi family invoked a series of old documents affirming their fief's sovereignty to escape the reign of terror.