Fleas are probably the most common carriers of tapeworm eggs. It's beneficial for the tapeworms because dogs and cats will pick at the fleas with their mouths, inevitably ingesting some (cats even more so as they also will catch some while grooming themselves). So then the ingested fleas that contain the tapeworm eggs are carried to the intestines, where they will hatch and live.
Fleas get infected with the tapeworm eggs as larvae. The larvae will swallow the tapeworm eggs (which are deposited by broken segments of tapeworm passed through the host's body) because they don't have developed mouths to feed properly yet. Note: That's why most flea treatments for furniture and carpets will target the larvae, keeping them from turning into adults.
Rabbits, and occasionally some small rodents, will eat the eggs as they are laid on grass.
Aside from tapeworms, flea bites can also carry the risk of causing a blood infection, which will either be expensive to treat (the only treatment I know of is a blood transfusion), or lethal. So in the long run, it's cheaper/safer to simply keep the fleas away.
Another, less lethal, reaction to fleas is Flea Allergy Dermatitis. It's when the animal is especially allergic to the flea's saliva and the body reacts harshly to it. It can cause itchiness will after the bite occurs. I've heard that it lasts for months, but I'm not sure how much of that is exaggeration. A couple weeks after the bite sounds more reasonable to me, but you could ask a veterinarian for a real number.
I'm not sure what damage would come from long-term scratching, but I can't imagine that it would be any good. If it scratches enough to break the skin you'd have to worry about infections and hair not growing back. All in all, I think it's cheaper and less risky to apply a poison to your pet than to subject them to the risks that come with having fleas.
Fleas generally don't go after people (probably just because of the general lack of hair, but maybe we just taste bad), but once developed from the larvae to adult fleas will bite the nearest warm-blooded creature they can find. From personal experience, I can say they will leave just as many bite marks as bedbugs at night.
All that being said, it's important to note that there are some risks of side-effects with the cheaper flea treatments. It's really important that you don't cheap out when buying medicine for pets. The reason the more expensive treatments cost so much is because they go through tests to make sure it's not harmful to the pets themselves. I personally think it's better to get flea treatments from vets rather than from stores for that reason.