I'm pretty sure that Brazil has the most Esperanto speakers in the world, but it also has a very large population. So, I'm curious, which country has the highest percentage of Esperanto speakers?
Vatican must have a very good shot to lead in the list by far, if only a single Esperanto speaker lives there. See: http://eo.radiovaticana.va/, RADIO VATIKANA - ESPERANTO REDAKCIO lists its address in Vatican City.
Then again, statistics get weird on fringe cases, Vatican is so small that it has more than 2 Popes per square kilometer.
I always tell people that Esperanto tends to be concentrated in areas where people feel the "language problem" most strongly - so we expect to find a higher concentration Esperanto speakers in Belgium than in the middle of the US. As I m sure you know, your question runs into many of the issues that questions about "how many Esperanto speakers are there" does. We have to determine what a speaker is and how to count them.
To get around this problem, I made a number of arbitrary and probably unwarranted assumptions. (See discussion at end of this answer.) Assuming that the number of hosts in Pasporta Servo (PS) at least loosely correlates with the total number of speakers, I picked a few countries and calculated the number of PS hosts per million inhabitants.
- Netherlands 2.15053763
- Sweden 1.69338451
- Ukraine 0.82544796
- Brazil 0.26744186
- USA 0.13620072
As I said, there are of course many arbitrary decisions and sources for error behind these numbers. Pasporta Servo might not correlate that closely with actual speakers for a number of reasons. I counted the hosts by hand and may have miscounted. I picked 1999 as the year to look at simply because that was the easiest list for me to find. My method did not account for multiple Esperantists living in the same house. Not a whole lot of thought went into which countries to count - I mostly picked countries that I knew had small populations or that had a high number of hosts. It's possible that in cities where there are lots of people, a smaller percentage become hosts because they don't see a need ... and the list goes on. I still thought this was an interesting way to look at the answer.