Image maps do this; often used with a real map, say of the USA, with towns marked and when you hover over each town it has a different link. Also used on photographs showing wseveral people and different links for each.
You can either do it over a background-image or over a normal image.
http://www.wickham43.net/imagemaps.php
Code downloaded to my PC will be deleted in due course.
WIN7; IE9, Firefox, Opera, Chrome and Safari for Windows; screen resolution usually 1366*768.
Also IE6 on W98 with 800*600 and IE8 on Vista 1440*900.