The Yukon Territory.
The continent that extends the furthest west is North America. On the other hand, the continent that extends the furthest east is Asia.
Virginia
The farthest north country is Denmark (via Greenland). The farthest east country is Kiribati.
The US State of Virginia extends further west than either West Virginia or New York.
Canada extends the farthest north and west compared to any other country. The northernmost point is in the Canadian Arctic Archipelago, while the westernmost point is in the Yukon Territory.
Maine is the state that extends the farthest east in the United States. Its easternmost point is West Quoddy Head, which is the easternmost point of the contiguous United States.
If you mean the island chain that extends from Alaska, that would be the Aleutian Islands. Note that the farthest west Aleutian island is closer to Tokyo than it is to Anchorage!
Kentucky is the farthest west.
Siberia is the farthest west territory. (It's also the farthest east, depending on which way matters to you)
Lake Superior is farthest west.
In the contiguous 48 states, Minnesota extends slightly farther north than other western states (Washington, Idaho, Montana, North Dakota).The farthest south is Florida, where the Keys extend below 25°N latitude, the approximate southern limit of Texas.