Stamen (stamen.com) is a San Francisco design and development studio focused on data visualization and map-making. Stamen heavily uses OpenStreetMap data in many of their map visualizations, and their developers have worked on many important tools and product offerings around OpenStreetMap. Some of these are described on their blog openstreetmap tag.
The tile servers are free to use, but usage restrictions may apply to heavy users. These are not updated from OpenStreetMap very often (data several years old ) but they have proven longevity, and are used by a lot of web maps. See tile servers for these and other options.