There are regions where people commute daily over the border, and even more where people commute weekly.

e.g. I have a colleague who lives in Malmö (Sweden) and commutes daily to Copenhagen (Denmark). Lots of people travel into Luxembourg every day.

When I lived in the UK, the director's family lived on a pretty island in Spain, and he went every Friday for the weekend. Not exactly good for his CO₂ emissions, but people do this kind of thing.

Yay, cheap airlines. When I was interning at Rutherford Appleton Laboratories in the UK, I met a cleaner who was flying back to Poland for the weekend every other week, to attend university ("extramural" is the proper term, I think?). I was pretty shocked that one can afford this on a salary of a cleaner in a government facility.

Europe is small in comparison to US and in EU borders virtually do not exists exactly like between states in US. You can go and work in any country in EU if you are EU citizen without any permissions or special paper. Plus there is a lot of countries like Czech, Slovakia, Slovenia, Austria, Belgium, Denmark, Luxembourg and couple more which are so small/have so good highway system that from any place in that country you can cross the border in under 2 hours which is basically like driving from SF to Sacramento or from NYC to Philadelphia. The point is that a lot of people travels cross country in Europe, very often it's they daily commute.