How do I sync all mail folders on my HTC Desire?
I'm afraid this is not possible with HTC Email application. This email app sync the "Inbox" folder automatically, but every other folder you have is not synced, the app gets all mail in the folder when you enter that folder to see what's inside.

You have the option to use K9Mail, a free e-mail client for Android which supposedly has support for push mail and sync of multiple folders.