What is the most northern state in the continental United States?
Since Alaska is part of the North American continent, it is the northernmost state.
However, if you mean the northernmost contiguous state, then it's Minnesota. Check this map.
http://geography.about.com/gi/o.htm?zi=1/XJ/Ya&zTi=1&sdn=geography&cdn=education&tm=17&gps=33_564_852_567&f=21&tt=14&bt=0&bts=0&zu=http%3A//www.lib.utexas.edu/maps/united_states/united_states_pol02.jpg