On Mac OS X Lion, in Safari, scroll bars are hidden by default. They are only shown when you start to scroll, using either the arrow keys or the two-finger-drag gesture. So if the page looks complete and you don't try to scroll because of that, you have no indication that there is more to the page.
Edit: the scroll bar is also shown briefly when the page finishes loading.
WorldWideWeb had scroll bars. Since day one of the web, browsers have been expected to gracefully handle documents with too much content to easily render on one screen. It's not reasonable for every author worldwide to have to simultaneously munge all their documents just because one browser maintainer woke up thinking it would look cooler for you not to know if there's more to read.