Make sure that the option is set in
Tools ->
Options ->
Preferences ->
Email options ->
Advanced Email options. Enable the option that says "Suggest names when completing To, Cc, and Bcc fields".
On rare occasions, the Suggest Names feature does not work because of a local nickname cache file corruption. If you are using Outlook 2003/2007 repair this problem by exiting Outlook 2003/2007, then open My Documents and paste %APPDATA%\Microsoft\Outlook into the Address window. Delete the file called Outlook.NK2 and restart Outlook 2003/2007..