Here are both fixes.
First, regarding the fixed sidebar, you need to give it a height for it to overflow:
HTML Code:
<div id="sidebar">Menu</div>
<div id="content">Text</div>
CSS Code:
body {font:76%/150% Arial, Helvetica, sans-serif; color:#666; width:100%; height:100%;}
#sidebar {position:fixed; top:0; left:0; width:20%; height:100%; background:#EEE; overflow:auto;}
#content {width:80%; padding-left:20%;}
@media screen and (max-height:200px){
#sidebar {color:blue; font-size:50%;}
}
Live example: http://jsfiddle.net/RWxGX/3/
It's impossible NOT to get a scroll bar if your content overflows the height of the div. That's why I've added a media query for screen height. Maybe you can adjust your styles for short screen sizes so the scroll doesn't need to appear.
Cheers, Ignacio