My goal is to build a task dashboard app which will pull tasks from different systems (e.g. Basecamp, Apple Reminders, ...) and display them in a certain way to a user. My biggest question so far whether there is any way how to access Apple Reminders with web application. I know it is possible via iOS app or OSX app. I guess I have to connect directly to Apple iCloud servers but haven't found any meaningful answer or hint how to do that.
Check this gem https://github.com/adammck/ruby-icloud. It's supposed to be an iCloud api in Ruby but it just supports reminders for now. So, you are a lucky guy ;)