BTC is not just open-source paypal. Its programmable currency. Not just in the meaning of the protocol itself but everything in the eco-system around it. This article is just a brief list of different resources currently being developed around BTC which allow for interesting concepts to be build using this coin and on top of the protocol.
Bitcoinj is a Java realization of the BTC protocol, that allows it to consist of a purse and sending/receiving transactions with no need in a local copy of BTC Core. It comes with full docs supplying and some teaching apps which tell how to manage the library. An example of the sucssesful working is provided here and shows in which way to write a simple app that forwards any money it receives.
Developed by Bitpay, one of the largest payments processing ventures currently operating in all BTC space, Bitcore is the one of new open sources JS library for making everything you can just dream of with the crytocurrency protocol. It is created to run both sides – client and server ones on node.js or interact with a secure BTC node even right in a browser(so called btc instance). An example of a project created with it is Insight, also the open-source blockexplorer. Check out both and see what you can build with it.