Excellent question. I think Yahoo!'s GeoPlanet can be very useful for this: they provide a pretty exhaustive list of places and the hierarchical relationships between them, and you can either download the list of names or use their API.
Other gazetteers (that's the term-of-art you're looking for) include GeoNames, which also has downloadable data free of charge. (I'm sure StackOverflow or even a Google search could get you more options along the same lines.)
Also, if you're planning to create a UI to let users select from your list of places, I like to suggest the Freebase Suggest plugin, a jQuery plugin that will force users to select from a certain category (in your case, countries, say) and provide a nice UI for choosing from what Freebase's semantic database considers correct. It even provides some wiki-like context to help with disambiguation.
