Given this div:
How can I make the scrollbars visible only when the mouse is
You can make overflow hidden until the mouse is over it, then make it auto. This is what I did ... note the 16px padding assumes a scrollbar is 16px wide, and is there so the text doesn't re-wrap when the scrollbar appears.
div.myautoscroll {
height: 40ex;
width: 40em;
overflow: hidden;
border: 1px solid #444;
margin: 3em;
}
div.myautoscroll:hover {
overflow: auto;
}
div.myautoscroll p {
padding-right: 16px;
}
div.myautoscroll:hover p {
padding-right: 0px;
}
See it in action at this fiddle - you'll want to widen the right side "result" window to see the whole box, or reduce the width in the css.
Edit 2014-10-23
There is now more variation in how systems and browsers display scrollbars, so my 16px space may need to be adjusted for your case. The intent of that padding is to prevent the text from being re-flowed as the scrollbar appears and disappears.
Some systems, such as newer versions of Mac OS X (10.8.x at least), don't show scrollbars until you start scrolling which could throw this whole technique off. If the scrollbar doesn't show you may have no reason to hide it until hover, or you may want to leave overflow as auto or even scroll rather than toggling it.