Mosquitoes suck. We all know this -- some of us more than others. If you live in certain parts of the world, mosquito-borne diseases could be a serious risk in your day to day life. If you live in the West or another highly developed area, odds are that mosquito bites are mostly just annoying, as opposed to a big risk. But with the migration of mosquitoes over the last few decades, even diseases that used to be limited to the tropics are now gaining ground in places like the US and UK. It's not an epidemic and there are medicines available in most cases, so there is no need to flat out panic, like so many people do these days. Simply use common sense and use mosquito traps to avoid putting you or your family at more risk than necessary.
This may not be common in the US or UK but it's a biggie, nonetheless. Malaria is caused by a protozoa. The disease does not actually originate in the mosquito itself -- it's passed after a mosquito bites an infected person. Not immediately, but rather about a week later when the parasite has had time to transition. Once infectious, the parasite is then passed on to the next person when the mosquito bites someone else. A few weeks or months later, the disease takes hold of the victim and treatment is necessary. This disease afflicts up to half a million people every year and kills between 1 and 3 million. Fortunately it can be cured.
If you're bitten by a mosquito who's carrying a filariasis worm, there's a chance of developing elephantiasis. And yes, the name has something to do with elephants, as that's the general appearance the symptoms take on. Swelling occurs in various areas and resembles an elephant. The disease is typically treatable but treatment will depend on what part of the world you're in. It typically occurs in the tropics.
This is a disease of the tropics and subtropics. Most people will recover naturally, but since there is no cure for those who experience a toxic phase, vaccination is standard in the parts of the world where it occurs. Nevertheless, some 200,000 people get it every year. If you're traveling to a part of the world where yellow fever exists, it's probably wise to consider a vaccination.
Dengue fever is another tropical disease but is far more widespread than the others, with an estimated 50 million people coming down with it every year. 50 million, and a few BILLION at risk! Pretty scary considering there is no cure for it. One can only seek supportive therapy in a hospital to treat symptoms, which include high fevers and lots of pain.
There are too many of these to go into big detail here, but you may be familiar with: West Nile Virus, St. Louis Enceph., Eastern Equine Enceph, Western Equine Enceph., Japanese Enceph. and others. These occur around the world and some of them in the USA. There is no cure for viral infections like these and you can only treat the symptoms. In some cases the disease is mild, in others severe, and sometimes people do die from them -- but it's not so common that panic should ensue!