OOcharts makes it easy to grab Google Analytics with a work around that would normally exceed the limits for Analytics' APIs. From the graphic below it's a simple 3 step process to get you to "data bliss." (Or, to misquote Joseph Campbell, follow your API and the data will open doors where there were only walls.) The OOcharts API returns both JSON and JSONP responses.
The sweetest part might what you get for the money: for $3 a month you get unlimited queries, unlimited API keys and 10,000 requests/month. According to the documentation, the API's core objects are API Keys, Queries, and Transactions. OOcharts consists of two parts: MIssion Control and the API.
By logging into Mission Control, you can create the access for websites you manage, create the queries and keep track of your transaction usage. Documentation also takes you through what successful and unsuccessful responses look like, how to set up to select a JSON or JSONP response, and shows a browser example.
From setup to the point of starting to get data is just minutes. Requests are queued for speed, and are also cached to save time. Examples are posted on Github.