The Aleutian Islands of Alaska cross the 180 degree-meridian longitude. This means that these islands are part of the Eastern hemisphere. This means that Alaska is the state that is farthest north, east & west in the United States!
If you don't believe in that technicality, the easternmost state is Maine, then Alaska retains it's northernmost and westernmost titles, and Hawaii rounds out the group by being the southernmost.
Of the lower 48 states, Maine is easternmost, Minnesota the northernmost, Washington the westernmost and Florida the southernmost.