well, I have 3 gmail accounts, 1 yahoo mail account, and a regular pop3 email account.
All worked well for me when I was on .10 and also now on .12
First is check the email settings like pop and smtp servers, socket numbers, and encryption. username and password. You email provider should have a support page explaining these items. next in the settings is how often the phone checks for new emails, and there are two schedules, like one for weckends and one for weekdays.
yahoo and google email is simpler, just username and password.
next go into settings and see if the accounts have sync enabled for email.
HTC has a widget called sync now, and another called auto sync. put both widgets on your home screen. auto sync should always be enabled. if not enabled, then that is your problem. next press the sync now widget and your notification area should show that syncing is progressing. look for any error messages.
good luck,
Howard