How do I reassign the F3 key to another application?

Solution 1:

FunctionFlip allows you to change the function keys individually.

Solution 2:

KeyRemap4MacBook does allow changing individual media keys.

Save something like this as private.xml:

<?xml version="1.0"?>
<root>
  <item>
    <name>Change Expose to F19</name>
    <identifier>B83A0F12-896A-42C4-AE87-1F24EE0B989E</identifier>
    <autogen>--KeyToKey-- KeyCode::EXPOSE_ALL, KeyCode::F19</autogen>
  </item>
</root>

Press the ReloadXML button and enable the remapping in the first tab.