In previous versions of OS X, scroll bars and scroll arrows appeared automatically in any window that is not sizable enough to show all of its contents. With OS X Mountain Lion however, scroll bars do not appear as often as they used to, especially if you have a Trackpad or a Magic Mouse installed.
Don’t worry though – if you prefer scroll bars to other navigation methods, you can bring them back: click the Apple Menu, click System Preferences and then click the General icon. In the section entitled Show Scroll Bars, click the radio button next to Always. The scroll bars will now always be visible.
Other options include displaying them based upon the input device and only when scrolling.