Rats can carry fleas. One of the most well-studied species of rat flea is Xenopsylla cheopis, the Oriental rat flea or tropical rat flea. This is the flea that carries bubonic plague.
Rat fleas can also carry rat tapeworms and a kind of typhus that affects rats and mice. These fleas do not attach themselves to humans unless they must. Under ordinary circumstances, rat fleas prefer to stick to rats and other rodents, but when no living rats are around, human blood serves them as well as rodent blood. This is how bubonic plague spreads; fleas leave a dead host and leap onto any living warm-blooded animal available, spreading the infection. The reason why they do not ordinarily attach themselves to humans is that they thrive in temperatures below 80 degrees Fahrenheit, but the human body temperature is much higher.