There are many potential hazards that dogs and cats (and other pets) can bring to your bed or that of your kids. Fleas and ticks are two common ones, both of which can bring serious diseases such as Lyme disease which is a serious bacterial infection commonly spread by ticks. In fact, having a cat or dog in the house almost doubles your chances of coming across an infected tick. The pet itself cannot spread the disease, but any live ticks it is carrying will. Dogs and cats can also bring bacteria such as campylobacter and other bacteria into your bed - including the bubonic plague (Black Death.) They can also bring parasites such as tapeworms and ringworm from feces and urine. This is not necessarily theirs, but can be carried from other locations in their fur. This is more likely with predatory cats than domestic dogs.