Oddity Central has a photo gallery of "Bat Predation by Spiders."
In most of the incidents recorded by Martin and Mirjam, the spiders were quite large, 10 to 15 cm legspan and one to seven grams in weight. A majority of the spiders were nocturnal web builders, spinning webs up to 1.5 meters across. Occasionally, groups of spiders got together to build several interconnected webs. Most of these webs were found near buildings inhabited by bat colonies. Only 12 percent of the spiders were able to catch bats without the aid of webs. Tarantulas in particular, were found eating small bats in the tropical rainforests of Peru, Ecuador and Brazil. The victim bats were quite small in comparison – 10 to 24 cm wingspan and three to eight grams in weight. A majority of these bats were small or juvenile insect eaters. Once caught, they usually died of exhaustion while trying to free themselves, or dehydration, or starvation, or even over-heating.