In Oregon you can check the web site to see if your vote was received. Not sure if they send an email, because my registration did not include my email address until just a few minutes ago ;-).

Aside from that you can't find out much more, of course, because as soon as your ballot is received and the outer envelope is scanned, it is discarded and your ballot (which is inside an inner secrecy envelope) is put in a box with the rest.