Address Book

Make sure the email address is actually in an email address field for the contact in Address Book, and not another field.

I'm wondering if you have the "use smart addresses" checked in your Mail preferences (under the Viewing tab)? If you uncheck that, it should display both the name and address.

Checking the field names was a great suggestion and was the source of my problems (I'm not the original poster). I had imported all my contacts from an Outlook export, and the emails ended up in a field titled "Other". You can cut/paste into Home Email and they instantly appear in the Mail/Address plugin.

+I see Home, work, home fax etc.+

If you follow down from first/last name and then company, the first two (work and mobile) are to enter phone numbers - "phone" is showing as a gray font; the next work (clicking on arrows reveals home, mobileme, etc) is for entering email address(es) - "email" is grey font. If you click on that gray font, the field will allow you to type in the email address. Entering the email address there will show it in Mail (if the smart addresses is unchecked).

If you click on the little "+" sign under the list of names, you should be presented with an empty/ready to fill in page and see the following on the right:

First Last (name)
Company
work -up/down arrows- (gray) Phone (that means you enter the phone number)
mobile -up/down arrows- (gray) Phone

work -up/down arrows- (gray) Email (that's where you enter email address)

friend -up/down arrows- (gray) Name (enter name here)
assistant -up/down arrows- (gray) Name (enter name here)

The Home street, zip, etc. will only show on an already existing address card and, the same principle applies as with a new card: the second "work" is where you need to enter the email address. If you have anything entered there other than the email address, click on it, delete that and enter the email address.

First to satisfy my curiosity - you said:

+I also put it in the 2nd work (below the company)+

What does the "also" mean? Did you enter an email address anywhere else? The 2nd work heading is the only place to enter email addresses.
And, by the way (as far as I know), it doesn't make a difference whether you enter the email address under (that particular heading) using work, home,etc; as long as you only have one email address for that person, the OS will use that one. If you have more than one, then enter the second one under the same heading, but under "home" if you used "work" for the first one (or vice versa).

I just checked my mail - new message:
if I have the "use smart addresses" unchecked, both the name and their email address showed; if I check the "use smart addresses", only the name will show. You can click on the name and you will get a pop-up window with several options.

If you address an email to a person for whom you have more than one address (I have one friend with 6!), all their email addresses should show up as you are starting to type their name so you can choose which one you want to use.

Aside from checking if you have the "use smart addresses" checked or not, also check - under "Composing" in Preferences - if you have the following checked:
"automatically complete addresses" and "when sending to a group, show all member addresses". I have both checked.

I hope that'll do it because I'm about out of ideas.....