It's "the USA", because the long form is "the United States of America". "The" here attaches to the "states", not to the entire name of the country.
Similarly, in "the UK", "the" is attached to the "kingdom"; and in "the USSR", it's "the union".
The Netherlands is a bit less obvious because people don't usually know the full name of the country. It's "The Kingdom of the Netherlands", and "the Netherlands" is just a geographic region - it literally means "the low lands", for obvious reasons.
In case of Ukraine, it's a bit trickier. The etymology of the word itself is from Old East Slavic "oukraina", which literally means "area at the edge" ("ou" - "at", "krai" - "edge"). When applied to geographic places and countries, it's the same as English "march", German "mark", or Polish "kresy" - i.e. "borderland", a region of some larger territory that is on the frontier. Which, of course, is what Ukraine was for Muscovite Rus - the borderlands with Poles, Ottomans, Crimean Tatars, and numerous small raiding steppe tribes; a place where life is harsh and violent, but there's no rigid state hierarchy;a place where criminals, runaway serfs, and anyone else who wanted to escape the oppression in Muscovy or Poland-Lithuania would go to join cossacks, because "there's no extradition from Don", as cossacks themselves put it.
Now, if you use it literally, as a descriptive term, then in English you'd put the "the" there - a literal translation of Russian "okraina Rossii" would be "the borderlands of Russia". So saying "the Ukraine" is basically saying that the country is the borderlands (by implication, of some other country). When you drop the "the", you are basically dropping the etymological baggage, and accepting the name as a proper name in its own right.
Depending on the language, this same distinction can manifest itself differently. For example, Russian doesn't have articles, but it has two different prepositions, "v" and "na" (roughly equivalent to "in" and "on" in English). The equivalent of saying "in the Ukraine" in Russian is "na Ukraine", and the equivalent of saying "in Ukraine" (without the "the") is "v Ukraine". Similarly to English, the "the"-equivalent form has been the literary standard for several centuries now, and is commonly used, but Ukrainians don't like it and prefer that the other form is used. This often results in lengthy flamewars on forums, Wikipedia etc.