Spiders work well.  I've had 2 insect problems in the past several
years.  One was with very small flies that were breeding in a house
plant.  Spiders handled that quite well.  They killed the flies - I'm
not actually sure what they were - they were smaller than gnats or
fruitflies and the other was a bee problem and frankly the only reason I
called in heavy artillery for the bees was because africanized bees were
a problem in that part of the country.

Interestingly enough though, the only death related to africanized bees
in that area while I live there was not directly due to their stings,
but a result of someone falling off a cliff while trying to get away
from them.