Keen.io is a backend-as-a-service that supplies analytics data through an API. This allows the developers of your site to create custom dashboard with your custom data. Their API works in 5 different platforms including native mobile platforms.
Google Analytics (https://developers.google.com/analytics/solutions/customize-extend)
Because Google is such a big player in this space they have also provided an API which allows creating custom visualizations using custom data. They also provide these tools for their App Engine customers.
BitDeli is really cool because it almost provides the best of both worlds. While the previous sites give you an API only type approach to building these custom analytics, BitDeli provides an API in three different technologies and also a dashboard GUI that allows you to also create and extend your analytics dashboard. They build some of the data for your which it reads from different sources and also lets you then extend that using their API.
MixPanel is a little different than the rest. They are a lot more like a conventional analytics tool but they offered some interesting features that got them an honorable mention on this post. Their website provides you with a SQL like feature that lets you create your own custom queries on your data which can be collaborated between all the users on the site. They also provide about 7 different API to allow you to track your data.
In conclusion if you want to have a very customized analytics strategy, where you are pulling in data from all sorts of sources from off-site warehouses to customer sent emails, you have several different solutions and tactics to use. These tools allow you to have more flexibility and complete control of what data you want to see. If you have an in-house development team you can change reports without having to wait for a third party service.