In South America, the bedbugs can fly and give you incurable heart disease by relieving themselves on your face.
These little horrors are called vinchucas, and are a bloodsucking subclass of assassin bug. They are not related to the common bedbug, but have evolved similar behavior and use the same feeding strategy (large, infrequent blood meals before molting).
The disease they transmit, Chagas disease, is a chronic parasitic infection that is imperfectly treatable even with expert medical care. Left untreated, it leads to chronic and degenerative heart disease. Chagas is a huge public health problem in Bolivia and throughout poorer areas of South America.
Unfortunately, the insect is beginning to show up in Southern California. The good people at UC Riverside are keeping an eye on it.