Some organization publishes a list. Check out page 54:
https://www.cafonline.org/pdf/World_Giving_Index_2011_191211.pdf
What are all those other countries besides the US doing at the top? What is the reasoning behind this?
I'm not sure what you're asking. The chart clearly says it is "Countries ranked by the percentage of population volunteering time". You even kind of named this thread that.
What exactly is it you don't understand?
Well, this is the list of top countries:
How come the list is essentially non-wealthy counties and then the US in the middle of them? I would expect that the countries with most volunteering be countries that are wealthier.
Depends on perspective, and it might not be the case that a more wealthy country volunteers their time compared to doing charitable work. Let's say there's a poor country and they work with one another, they can't pay one another, so they volunteer time to help one another out. It may have to do with economics, may have to do with culture, or both factors.
I don't see why they must be correlated.