Outlook shows the sender's display name in the From field and the only way to see the actual email address is by opening the message, then right-clicking the name and then choosing properties. (Outlook 2002/2003 may show the email address as well as the display name when you open or reply to a message.)
You may be able to see some addresses if you use the Have Replies Sent to field - right click on the row of header names and choose Field Chooser. Choose Address fields from the dropdown where Frequently-used fields is shown. Drag "Have Replies Sent To" to the row of field names. (Choose Custom on the r-click menu if using Outlook 2003 and a multi-line view, then Fields.)
A better solution is the free utility, Recipient Info, from Ornic.com that lists the addresses in a dialog box.
To use it, select a message, click a button (or use the Tools,
Recipient Info menu) and see all of the addresses on the message
in table format. (This add-in works with all versions of
Outlook, although it may report errors when you start Outlook
2003.)