For things stored in open sheds or outside, wasps are probably the
biggest worry, but they usually give significant warning and you'll
probably get your first sting well before you get close to the nest.
Last time I checked, yellow jackets were the leading "direct" cause of
death by insect (i.e. not counting insect borne diseases) in this
country.
Honeybees, while much more docile, will make a mess of a machine if
they take up residence for too long. Fortunately it's easy to find
someone who will take them off your hands. A healthy colony might be
worth a couple hundred bucks to a bee keeper. Or you might want to
keep them yourself. They're pretty good at keeping wasps from
building nests nearby.
Black widows will depart if you open their hiding place to the light
for any significant length of time. I wouldn't let them hang out in
your house, though, especially if you have cats. Cats are especially
susceptible to black widow bites.
Rodents are probably my biggest worry due to the diseases they carry.
(Plague, Hantavirus, ...)