For most of the history of Safari, although the browser did not provide a way of erasing all cookies at shutdown, the facility could be emulated by setting one's ~/Library » Cookies » cookies.plist file to "read only" (see this hint). Since cookies are stored in memory until the browser shuts down, the result was a perfectly normal browser session with no cookies carried to the next session.
This ability went away with 10.5, as a read-only cookie file caused random issues at most sites requiring a login cookie. There was no option but to reset the cookie.plist file to read/write, and delete them by hand every now and then.
The problem has been resolved in 10.5.6, but the technique for achieving it is slightly different -- you now must set the containing folder to read-only, not the file. Read on for a detailed walkthrough, if you need it...