Legal use of map tiles
We are currently using http://server.arcgisonline.com/ArcGIS/rest/services/World_Street_Map/ and I highly doubt that this is legal - we don't have any account or contract with them.
I also don't understand the TOS and they seem to change sometimes.
There is:
Use ArcGIS Online maps and map layers, imagery, and geometry services in conjunction with Esri software or an ArcGIS
Online subscription for projects and applications that are both internal and external use
As long as you do not exceed the transaction cap if the cap applies to you.
Government, Education, and NGO users: Full unlimited use
(http://downloads2.esri.com/ArcGISOnline/docs/tou_summary.pdf)
But also
ArcGIS Online paid Developer Plan accounts or Development and Testing Plan accounts:
License may use one (1) million map transactions per month in conjunction with their account. One (1) transaction is equal to eight (8) map tiles.
(https://developers.arcgis.com/terms/)
We should also include piwik to generate better usage data on maps - or see if our google analytics which is still in there is good enough (I don't have the account data)