We are in principle happy for our map tiles to be used by external users for creative and unexpected uses - in contrast to most web mapping providers, which insist that you use only their supplied API.
However, the OpenStreetMap servers are run entirely on donated resources. They have strictly limited capacity. Heavy use of OSM tiles adversely affects people's ability to edit the map, and is an abuse of the individual donations and sponsorship which provide hardware and bandwidth. As a result, we request that users of the tiles abide by this tile usage policy.
You should read all of the details on the tile usage policy page.
You might also consider making a contribution to OpenStreetMap to support the infrastructure upon which you are relying.