Looking in the Azure portal, I can see monitoring charts for API apps and Web apps that return information on metrics such as number of requests, cpu time, data i/o, etc.
Is there an API that I can query that will return information on Azure app services?
If you just want to see the list of web apps within a resource group, this can simply be achieved using the Azure Resource Manager API, which is the default API used by the new portal.
We now even have a cool tool to explore these APIs, check https://azure.microsoft.com/en-in/blog/azure-resource-explorer-a-new-tool-to-discover-the-azure-api/
The API Reference itself is at https://msdn.microsoft.com/en-in/library/azure/dn790568.aspx