Sounds like you are referring to the autocomplete feature. This is turned on by default in Outlook 2003. Here is more detailed info from Outlook Help:
How does AutoComplete work?
The AutoComplete feature is turned on by default, and displays suggestions for names as you type them in the following situations:
To, Cc, and Bcc boxes in an e-mail message.
To boxes in meeting requests, tasks, and share requests.
E-mail field in a contact card.
When you type the first letter of a name in one of these boxes, AutoComplete begins to suggest possible matches based on names you have typed before. The more letters you type, the greater the possibility of AutoComplete finding a match.
Click the name you want to enter in the box. If you are using the keyboard, select the name using the UP ARROW or DOWN ARROW keys, and then press ENTER (or TAB). If no suggestion matches what you are typing, continue typing. The AutoComplete feature will remember what you typed the next time you type that name.
Names that you use less frequently will move lower in the list over time, and eventually will no longer appear.
Delete a name from the AutoComplete list:
Select the unwanted name or e-mail address by using the UP ARROW or DOWN ARROW key.
Turn AutoComplete off:
On the Tools menu, click Options.
On the Preferences tab, click E-mail Options, and then click Advanced E-mail Options.
Clear the Suggest names while completing To, Cc, and Bcc fields check box.