The accepted answer by New Alexandria is a great one; it goes into detail, so I don't have to. I'll just say that, for those reasons, in general it's very bad practice to hide the scroll bars. It's a very familiar feature, and familiar features come with user expectations—mess with those expectations and you generate confusion.
Even though Apple does it; there's a reason why they let you change this behavior in System Preferences » General. However slight any confusion may be, confusion is always bad. And for computer illiterates, the confusion may be greater than we think.
All this, of course, assumes that you're not creating some sort of poetic software and wish to arouse these particular emotions. I can't think of an example.
But the bottom line is that it depends. It depends on your application, your users, and the circumstances surrounding them. Even for me, it's annoying to have to scroll to make the bars visible before I can drag them—but I use a Magic Trackpad, so I like them hidden (hence it depends on the user).
A great example is Pentadactyl for Firefox, an add-on that gives you Vim key bindings and a Vim-like status bar, and lets you do everything with your keyboard. You scroll with
k, and the status bar shows the scroll position. Now it suddenly makes sense to hide the scroll bars.
Here's a screenshot. On the right side of the status bar, it says "Top." (The image is from a blog post I wrote about it—original):
Once you scroll, it shows your position as a percentage value. Here's a second screenshot, taken right now (original):
But, note that scroll bars are still useful and visible in areas such as
textareas, like the one I'm typing in. Here, they are still expected. It all depends on the situation and circumstances.
Every year, my father is impressively getting more efficient with his Mac. Still, he has a tendency to drag the bars rather than "touch scroll" with his Magic Mouse, and always uses back and forward buttons. However, his mouse at work has a physical scroll wheel, and that one he uses. Perhaps because its purpose is more obvious—more familiar, no confusion.
Is hardware and software design moving too fast and leaving some of the less literate users behind—or is it a natural and necessary pace which they must choose to keep up with? Well, I suppose it depends on your target audience.
Disclaimer: I'm not affiliated with Pentadactyl. It, and Vim, are simply great examples.