BCX.RB is a full-fledged Ruby client that wraps the Basecamp Next API. Though not officially built by Basecamp's provider, 37Signals, BCX.RB is endorsed by Basecamp on their GitHub channel and developer site. Though it is usable, the wrapper is lacking endpoints and thus it's coverage of the Basecamp API is partially incomplete. Community contribution is encouraged. The following API resources are supported and have been tested using the wrapper: People, Projects, Todolists, Todos, Accesses, & Authorization.
Slack, a popular collaboration tool that helps teams streamline communication and eliminate email clutter, has set its sights on becoming the default messaging platform that developers will integrate with. Slack officially announced the Slack Platform at a recent Launch event.
DoneDone, issue tracking service, offers the DoneDone API that enables developers to include DoneDone's feature set via existing workflows and third party applications. DoneDone's premier goal is to streamline and simplify projects and eliminate the use of spreadsheets, sticky notes, email chains and other traditional forms of cumbersome notes and reminders.
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.