The very core of what makes Gmail so enjoyable is that their expertise in free form search allows me to pretty much stop caring about organizing my mail at all. I generally just hit archive, and rely on search to retrieve whatever I may need to later. No web mail client can provide such a service against encrypted mail.
At the same time, it is Google's access to my mails' content that allows them to show me 'relevant' ads. Without this ability, providing Gmail for free will get a lot harder to justify.