I came into a problem on one of my machines where the WordPress permalinks were not working. Typically, I go to the WP backend and click Settings >> Permalinks, then resave what I have there so that WP updates the .htaccess file. However, that did not do the trick this time.
After some digging, it turns out that the “mod_rewrite” capability was off – probably as a result of recently upgrading to WAMP 2.5. It’s really easy to fix too – under the WAMP tray icon, just click Apache >> Apache Modules >> rewrite_module. Found the solution within this SO question.