People would generally tend to be surprised if they didn't get a confirmation email of changing password.
Not only does it serve as the early security alert option for those who may have had their account altered by others, but it also serves as a confidence booster for those who did genuinely change their password. Note that the email has to be immediate and high priority - not just deferred to some bulk email sender on a chron job every hour or at the quieter periods of the day.
But it's also very important to provide some information to the user about what to do if it wasn't them who changed the password. There's little point telling the user their password was changed and not guiding them on the next stage of the process should they need it. It's critical that the next steps can be fast-tracked with simple clear steps, using calming language, as the user will likely be in panic mode at that point.
If I didn't receive an email confirmation, then I would wonder whether it had worked. I might feel I'd have to log out and log back in again with the password to confirm it worked. This can be mitigated to some extent by on screen messages that say 'your password was successfully changed', but to receive the email to my correct email address to let me know is a great confidence booster, because it seems more confirmational than a 'yeah whatever, done that' message on the website.
The email is also a good opportunity to provide a little extra information about accessing their account if it's relevant, but never ever use a confirmation email like this as a marketing ploy.
It also serves as a gentle reminder (especially to people who have had accounts for a while) of which email address is being used. Not receiving a confirmation email might make me wonder which email address is being used, and if the email went astray. This is more the case when you don't receive emails from this service very often anyway.
In many cases where you can choose what kind of email notifications you can receive from a service, these administrative emails are still not able to be switched off. This is true for Twitter, Facebook and others - you cannot opt out of emails about your account, your security or your privacy.
Would they expect to see a confirmation email? Generally yes - and increasingly so
Should they see a confirmation email? Absolutely