I crossed the US-Canada border by bike once, during a group ride which started in Vermont. We were spending the long weekend in NH, with a group and this was the second day ride. We stopped and ate lunch in park just short of the border and a few of us rode over the border and back, maybe 5 miles. This was in 2005 and there was no passport required. I really don't remember the names of the border towns, but it was fun. On the way back, the US border patrol agent asked me all kinds of questions about where I lived, even though he had clearly seen me and the others ride over the border into Canada, just 10 minutes earlier.
Riding over the border from the Czech Republic to Austria was quite fun and took about 5 minutes. They are used to people crossing on bikes. It felt like you were going from the 1950s to the present time in a second.