Don't give it up to other creatures: mold, termites, vermin! Current science indicates that crawlspaces perform better when treated like indoor spaces: mini-basements, if you like! The old way was to leave vents open and insulate the floor with fiberglass batts (unfaced is best: I often see the vapor barrier on the wrong side). This allows for drastic fluctuation in temperature and moisture and many openings for critters. Today's solution is to insulate the walls with fire retardant foam board (leaving a three inch gap at the top to check for termites), seal and or remove the vent openings, cover the floor, and preferably the insulated walls too, with a tight vapor barrier (see other post below), include a sump pump and or drains to prevent flooding, and provide conditioned air to the crawlspace from your HVAC system.
Basically you treat a crawlspace as either an outdoor space or an indoor space. Most of the time I find they have an identity crisis. For example, his one below had all the vents closed (indoor space) and spray foam insulation on the joists (outdoor space). The spray foam also makes it impossible to assess the condition of anything it covers. Since the vents were closed, there was nowhere for the moisture to go. The cold ducts were dripping with water. My suggestion for remedy was to insulate the walls, add a tight vapor barrier and crawlspace door and open one or two registers to the ducts to make it into a consistently indoor space.
BEFORE
AFTER
Click on Image for link to Building Science Article
These half inch gaps are caused by damp crawlspace below. Could spend thousands on new floor when it would just happen all over unless crawlspace ventilation was improved.