The Basecamp 3 Laravel PHP SDK by Claudio Gonçalves Malaquias allows developers to integrate the Basecamp 3 API into their applications built with Laravel 5, a PHP web framework. Documentation is provided in Portuguese.
Nathan Kontny is out to revise how you write, especially when you work with others. His online word processing program, Draft boasts features you can't find in any other wordprocessor--like a professional editing service, for example.
Celoxis is both an online and installable project management platform integreted with Microsoft Outlook, iCal, Google Calendar, and Salesforce.com, among others. Celoxis explains the Celoxis API in a way that suggests they want you to be able to use it easily.