Speaking as someone who reads other people's email as part of my job, it really, really, REALLY depends on what your mail environment looks like.
The short answer is:
If they don't want you to know, generally there is a way to prevent you from knowing about it.
Exchange with Outlook
The system does track the Last Logged In user for a mailbox, but that attribute isn't easily viewable without the Admin Tools. The Admin Tools that would be used to view the same mailbox.
Generic IMAP4 + Thunderbird
Unless the mail administrators have taken the effor to publish your last login list somewhere, the only way you'll know is if mails get their read/unread status changes, or mail moves mysteriously.
Google does in fact publish the last few IP addresses that logged into the account. Its at the bottom of the page. Check that, and if you find addresses you don't know about, it's a good sign that something strange is going on.
Generic Corporate email systems, not just Exchange
All incoming mail is copied to a specific address. Or perhaps only people of interest. Since this copy happens while the mail is still just a text-file in a mail-spool somewhere, you'll never know. This kind of setup is very, very common in E-mail Archiving setups.
Steps to take
Changing your password is a good first step if the mail is being monitored by an actual login. It won't help if the mail is being copied out of a mail-spool before it actually gets into your mailbox; there is exceedingly little you can do about that scenario. If it happens again after your password has been changed, then something else is going on, and it's time to take it up with your mail administrator.