I was looking at Gunnar Garfors's 25 Least Visited Countries in the world. I had always wondered about this, so for fun I decided to compare the tourist numbers he provides against the countries' populations, areas, population densities and per capita income. There is not a strong correlation for any of these, but population had the strongest with r^2=0.15. Grouping countries by island vs. landlocked vs non-landlocked, island countries had a lower average visitation rate.
The real relation is likely going to be an equation of cost and payout - that is, the average cost of visiting, versus what people think they'll get out of visiting there. Countries that are safe with developed tourist infrastructure (which per capita income is a proxy for) and good promotion (which increases the perceived value) and at least tolerable climate will be the best in terms of payout, but the average cost is going to be more complicated - to get lots of tourists, you need lots of countries relatively near you with money, and minimal administrative barriers (i.e. no unfriendly ergo uncooperative political relationships.) This reads like a description of Europe, and not surprisingly, 6 of the 10 most visited countries are in Europe, and the U.S. is the only one in the western hemisphere. If you wonder if local culture is in danger of being destroyed by all these tourists, most-touristed-country France has more tourists per year than its total population, and French culture seems to be in no danger of disappearing. If you're wondering, North Dakota is the least-touristed state in the U.S.