Surprisingly enough it is not required. The rule says the fielder may wear a glove but it doesn't require it. Once worn it must meet certain specs.

Sara,

You'll learn a lot of interesting things about baseball's rules when this venue gets cranked up after people switch over here from Eteamz.  I've been umpiring for ten years now, and just when I think I know all the rules, I learn something new.

What makes it even more frustrating about the rules (from an umpire's perspective) is that they are subtly different from organization to organization.  With respect to gloves, for example, professional baseball doesn't require that the catcher wear a catcher's mitt.  He could wear a first baseman's mitt or glove, or even go barehanded.  LL Baseball, OTOH, mandates a catcher's mitt (and ONLY a catcher's mitt) for all its divisions.

Manny