Styling lists/widgets in the sidebar

My sidebar outputs widgets in <ul> format. Is it possible to style each <li> within that <ul> so that the background colours alternate?

Somehow, I’ve got to get every other <li> to read <li class="odd"> in order to style it in my CSS. But how do I get the widgets to append this class to every other <li>?

I presume I’d have to add some code to functions.php to do this. I’m not sure what to do, though.