When you change your password, you're usually required to enter both the old and the new one. This is when the check is usually performed.

What I'm more worried about is the system that some Polish banks use, called masked passwords over here. With this system, you're only required to enter certain characters of your password, but the set of required characters changes at each login. This exists to make key loggers much less effective. There's apparently some hashing going on (something to do with curves and polynomials), but I couldn't find more details when I last looked.