A Seventh Circuit opinion remarks on what to call the country (which happens to be where I was born, though it wasn't an independent country back then):
There continues to be confusion over whether to use the article “the” in connection with “Ukraine.” In the briefs, Gutnik’s counsel uses “the Ukraine,” while the government uses “Ukraine.” Likewise, at joint remarks in January 2005, Vice President Cheney used “the Ukraine,” while President Yushchenko, the elected leader of the country, used “Ukraine.” See Press Release, Office of the Vice President, Vice President’s Remarks with Ukrainian President Yushchenko (Jan. 26, 2005) (Villa Decius, Krakow, Poland). We will use Ukraine, which is not only correct but is also preferred by Ukrainians themselves, see Associated Press, Terminology of Nationalism, N.Y. Times, Dec. 3, 1991, at A10, and is the grammatically consistent choice, see Andrew Gregorovich, Ukraine or “The Ukraine”?, FORUM Ukrainian Review No. 90, Spring/Summer 1994.
I say "The Ukraine," because that's how I learned it; I take it Cheney learned it this way, too. Interestingly, though Russian doesn't have articles such as "the," there's a similar controversy there — for most areas, you'd say something is in the area ("v Pol'she, v Angl'ii," "v" meaning "in"), but for the Ukraine, you'd say something is on it ("na Ukrain'e," "na" meaning "on"), or at least that's how you said it when I was growing up during the Soviet era. Nor was it just a country vs. area-in-a-country distinction; you'd say "v Litv'e," or "v B'elorussii," but "na Ukrain'e").
My sense is that this was because "Ukraina" wasn't just a place name, but also retained part of its non-place-name origins, in the sense of "borderland." It might also explain why Russians are quite comfortable with the "na Ukrain'e" / "the Ukraine" usage, and (as best I can tell) many Ukrainians prefer "v Ukrain'e" / "Ukraine" usage, which focuses more on the country as a country like any other rather than just the borderland of Greater Russia. I'll probably keep saying "the Ukraine," perhaps because I'm culturally much more Russian than Ukrainian (I'm still more American than Russian, but that's less relevant here), but my sense is that the tide is turning against it overtime, just as "the Lebanon" and "the Sudan" have in the past.