From some US states, one may travel straight south and get into some Canadian province or territory (of course without crossing the equator).
What are these nine "US state $\to$ Canadian province/territory" pairs?
Assuming that one state to two different Canadian territories counts as two pairs (and by the presentation of the question, I think it does), then Novarg actually has six, and I think I have the other three.
Point Roberts, Washington is directly north of Saturna Island, British Columbia
A large portion of the border between New Hampshire and Quebec is defined by Halls Stream, which leads to several small points along the border where NH is directly north of QC, particularly near the north end of the river.
Mt Hubbard, in the Saint Elias Mountains, lies on the border between Alaska and Yukon. The border travels roughly SSW from there to Mt Seattle, so the Alaskan area around Mt Hubbard is directly north of Yukon.
The main difficulty with this question was finding the specific points. Most of the US-Canada border is defined strictly by latitude and longitude, so it is impossible for those areas to have part of the US directly north of Canada. This eliminates Idaho, Montana, North Dakota, and Vermont as possibilities, as well as the Minnesota-Manitoba and New York-Quebec borders.
That leaves eleven pairs of US states and Canadian territories that share a border. Ohio and Pennsylvania only border Ontario along Lake Erie, so they clearly don't fit the requirements either. That only leaves nine border pairs. And since your question says that there are nine pairs in the answer, these must be them:
Here are the ones I found so far:
1. Alaska, Prince of Wales Island -> Graham Island
2. Minnesota, Voyageurs National Park(where Kettle Falls hotel is) -> Oakpoint Island/Kettle Island/Moose Island/etc(I guess those islands count as one territory, there are 6 islands according to google maps)
2.1 Minnesota, Norway Island/Burnt Island Campground -> Some unnamed Canadian ground(but since it's still Minnesota, I guess it doesn't count as 3
3. Michigan, Detroit -> Windsor, Ontario
4. New York, Buffalo (very west part of it) -> Niagara falls/St. Catharines
5. Maine (the part that stick out north, either very west or very east) -> Quebec at very west and Fredericton at very east