To expand on the previous two answers: the .screenrc line
termcapinfo xterm* ti@:te@
will turn on your scrollbars. This is a win unless you're using control-A to switch between multiple screen sessions in the same Terminal window. Screen uses what's called cursor addressing mode to keep a separate history buffer for each session; the termcapinfo line above tells it never to use that mode. All history then goes into one buffer, the native Terminal buffer, and you'll see lines from all sessions mixed in with each other.
These days that just means using a separate Terminal window (or tab) for each login on your remote -- a low price to pay for getting your scrollbars back, to my mind.
So why isn't scrollbar mode the default? Because in Ye Olde Tyme Dayes when we walked twenty miles in the snow to our 80 by 24 character-cell VT100s, you could only get one login per terminal. Unless you had two terminals on your desk, screen was the only multi-session game in town.