One thing that comes up often when discussing "what-ifs" with family or friends is why the British government never nabbed Alaska when Russia had placed it up for sale and made it into Canada's fourth territory. Was it bad timing (Canada gained self-governance that year), lack of money (hard to believe with an Empire of that size), or lack of interest? Or indeed another reason that I haven't thought of?
Because Russia had been at war with Britain for most of the preceding two decades.
One of Russia's problems in owning Alaska was defending it against it being used as a British route to invade Russia (militarily insane - but that's politics) - remember Canada was British at the time.
By selling it to America they installed one of Britain's adversaries in the way
Russia and America (the Union) were very nearly allies during the Civil War. The implied enemies were not so much the South (Confederacy), but rather Great Britain and France, who threatened to intervene on behalf of the South, and who had fought Russia a few years earlier.
Although Russia wanted to "monetize" Alaska, she also wanted it in "friendly" hands. The (re-united) U.S. fit the bill. Great Britain did not, after having allied with France and Turkey in the Crimean war.
The following might explain why the British did not try to acquire any American possessions anymore: http://en.wikipedia.org/wiki/Monroe_Doctrine.
In brief, the Monroe Doctrine, introduced in the 19th century, is a statement by the United States that they would consider any European attempts to colonize in or interfere with North/South America as hostile, and respond accordingly. Conversely, the U.S. would not interfere with current European holdings.
The Monroe Doctrine was introduced in 1823 and Alaska was purchased by the United States in 1867.