Not only are there a number of single-border countries — countries that only border one other country — but there are three countries within countries. Personally, I’m holding out for the holy grail of single-border nationdom, the Inception border: The country within a country within a country (keep working at it, Austin, Texas, you’ll get there someday!).
CGP Grey, the creator of the popular Bizarre Borders video featuring Canada and the United States, actually started the series off with this video on single-border countries. It’s hard to watch this and not wish all of your learning could be crammed into hyper-informative 2-minute increments.