New Brunswick
There are two Canadian provinces that border Maine. The one that borders Maine on the northwest is the province of Quebec.
New BrunswickNew Brunswick forms the entire eastern border of Maine. Also of note is that Maine is the only US state that borders only one other state, which is New Hampshire.
The Canadian province that borders Maine to the east is New Brunswick. The capital city of New Brunswick is Fredericton.
The only Canadian province which borders Michigan is Ontario.
Quebec... From about the northern tip west is Quebec, and to the east New Brunswick.
Vermont borders the Canadian province of Quebec to the north.
Alberta and Manitoba.
BC
Ontario
British Columbia
As google maps easily tells you, several states do. Maine, New York, Minnesota, and North Dakota. Then Montana borders 3 provinces, and Alaska borders one province and one territory.
The US state of Minnesota is bordered by the Canadian provinces of Manitoba and Ontario to the north.