If you own a moped, you might need to buy moped insurance.  Depending on what state you live in, and how big your engine is, you may be required to have insurance on your moped.  Regardless of your state requirements, it may be a good idea to have insurance just for protection sake.  If you get in an accident, or your moped gets stolen, it can prevent you from spending a lot on repair and recovery costs.  Your local DMV (Department of Motor Vehicles) or government agency can answer your insurance questions, so check in with them first.  If you do end up needing insurance, then you probably have to officially register your vehicle as well. 

If you find out that you want moped insurance, there are a wide variety of insurance plans to choose from.  Definitely shop around for the best rates, as different companies will have different policies to offer you.  Your rate will depend on your driving history, experience, how populated your area is, how expensive your 50cc moped was, the weather conditions in your area (rain/snow), and other things as well.   Some policies may require you to wear helmets, and have other safety equipment in place when you are driving.

It can be a time consuming activity to shop for and compare moped insurance plans.  Keep in mind that the cheapest policy isn't always the best deal.  Weight the pros and cons as far as how much coverage you are getting.  Absolutely use the internet to your advantage, as you can find a lot of information and ask a lot of questions without leaving the comfort of your own home.  Search for online coupons and research the companies and customer feedback before you isgn up for a policy.  Read the small print and you should be in good shape.