I had the same problem after upgrading to 2.1 from 1.5. All my SEF urls would work except for
www.mydomain.com or
www.mydomain.com/index.php.
After reading numerous posts here and trying various .htaccess fixes I came up with a solution. I realised after looking at a debug of the site that the the component wasn't finding any result for:
SELECT * FROM jos_redirection WHERE `oldurl` = 'index.php' AND `newurl` != '' LIMIT 1
So, I just added two entries in the Custom URLS to redirect to my home page of choice, one with the New URL empty and the other with just 'index.php'.
I am not sure if that is an official solution but it worked for me.
As a side note, I think I am my problem was related to the fact that I'm not using the com_frontpage module as my homepage.