The main OpenStreetMap servers that contain the database, the main API and other services (like osm.org and it's main map) are managed by the OpenStreetMap Foundation (OSMF), which also takes care of other "official" stuff. The OSMF is mainly funded by membership fees as well as donations.
However, by "OpenStreetMap" you may also mean the community in general, which itself provides a lot of services, that are funded in many different ways. Sometimes the hardware is provided by companies (e.g. the FOSSGIS servers that run several different community projects) other projects are completely privately financed by the people who run them.
You may also refer to how creation of the software that is used in OpenStreetMap is funded, like the API or the editors. All these software projects are usually written and maintained by random people in their free time.
The OSM hosting and servers are paid by the OpenStreetMap Foundation and donators. Membership costs £15.
answered 17 Jul '10, 11:59