how can i tell if and when a user received an email?

You should use the message tracking centre.  This gives you the most information, however if an intermediate SMTP server has been used then it only indicates that delivery has been achieved to that server.  It also doesn't indicate whether the user has collected the e-mail from the mail system.

Enable it: http://support.microsoft.com/kb/246856
Use it: http://www.msexchange.org/tutorials/Exchange-2003-Message-Tracking-Logging.html

Thank you Steve, but I have not yet enabled the Message Tracking Center and I would like to check on 3 specific messages already sent and received over the last week.

Your best bet is to look at the headers of those messages

You cannot tell from those sent unless you either have the SMTP logs or the message tracking enabled.  However, if Exchange is configured with default settings then you would get a message from Exchange indicating delivery was delayed within about 48 hours if delivery was not achieved earlier.

For received messages, you can look at the message headers in Outlook.  See this article: http://office.microsoft.com/en-us/outlook/HA010937071033.aspx

I can see I didn't explain this clearly.

I would like to see if another user has received an email sent to them 3 days ago.  I could assign myself rights to their mailbox but I would prefer not to if there is another way.  I don't want to snoop inside their mail, I want to find out if a specific message was delivered to their mailbox and if so, when.

Next, the user claims to have sent a specific email, also 3 days ago.  Is there a way to see if that is true, and if so when it was sent?

Thanks for the points.  I've been away for a while, sorry for the late reply!