PhoneView does just what you want: let's you browse your iPhone's whole file system without having to jailbreak, using an OS X desktop app. It also lets you view all of your SMSs and Notes and save them to your computer, and even add new notes from the desktop. PhoneView is not free though. I bought it and can attest that it works great.
http://ecamm.com/mac/phoneview/
I actually have my iPhone jailbroken, so I didn't buy PhoneView for filesystem browsing. I mainly bought because I wanted full access to my Notes and SMSes from my desktop. The filesystem access was just a bonus.