These cover the bulk of countries outside Europe. Forex brokers catering for India, Hong Kong, Qatar etc are likely to have regulation in one of the above, rather than every country they support. Some brands are regulated across the globe (one is even regulated in 5 continents). Some bodies issue licenses, and others have a register of legal firms.
Non-bank foreign exchange companies offer currency exchange and international payments to private individuals and companies. These are also known as "foreign exchange brokers" but are distinct in that they do not offer speculative trading but rather currency exchange with payments (i.e., there is usually a physical delivery of currency to a bank account).
There are actually three ways that institutions, corporations and individuals trade forex: the spot market, the forwards market, and the futures market. Forex trading in the spot market has always been the largest market because it is the "underlying" real asset that the forwards and futures markets are based on. In the past, the futures market was the most popular venue for traders because it was available to individual investors for a longer period of time. However, with the advent of electronic trading and numerous forex brokers, the spot market has witnessed a huge surge in activity and now surpasses the futures market as the preferred trading market for individual investors and speculators. When people refer to the forex market, they usually are referring to the spot market. The forwards and futures markets tend to be more popular with companies that need to hedge their foreign exchange risks out to a specific date in the future.