This applies to Apple Mail on OS X as well as the mobile Mail application on iPhone, iPod Touch and iPad. It will also apply to any mail application that cannot auto detect the IMAP Path prefix. If you are seeing this problem on an unnamed mail client, you can assume that the solution described here will work for you, but you will need to do a little legwork to find where the option resides in your program.
As described in our email configuration articles, you will need to set your IMAP Path Prefix to INBOX to solve this problem. Make sure you use all capital letters.
On OS X:
On iOS4:
The steps to do this will be very similar on previous version of iOS for the iPhone, iPod Touch and iPad.