This is an adaptation of Cody Sechelski's Create a Calendar View in Salesforce.com.
The main problem with his implementation was that it wasn't handling more than 2000 records. This was due to a Apex workaround, as it is reserves start and end variables, Cody made a repeat table and parsed that into JavaScript object. My solution creates JSON string in Apex and then uses string function to replace all startString and endString instances. A more sensible solution would involve recreating the object in JavaScript or simply editing the FullCalendar library to look for different variable names.
I have also simplified the code a bit so you can start working towards your personal implementation. As this is using JavaScript remoting, I hope this gives you a framework to work towards more advanced features like editing or optimizing request sizes (executing a request on next month load).
The page
<apex:page showHeader="fals