Beginning with OS X Lion 10.7, Apple changed the behavior of scrollbars to disappear when not in active use. This brought OS X in line with the behavior of iOS. Personally I find this annoying because I can’t glance at the screen and determine which areas are scrollable. I can forgive this in iOS because the iPhone screen is so small that every pixel counts and there is typically just one scrollable area, but on a Mac I’d rather sacrifice a few pixels for this function. For those of you with a Mighty Mouse with the notoriously stuck scroll ball this tip might be especially useful.
To restore your scrollbars, go to the Apple menu > System Preferences > General. Near the middle of that panel is the option for “Show scroll bars”. Switch this to “Always” and enjoy your scrollbars!