Recycle Bin is coming into Moodle core with Moodle 3.1, which is scheduled to be released in May 2016, thanks to Moodle Users Association for taking it as the very first project.
Currently, the Moodle Tracker issue – MDL-48012 i.e. “Integrate the ‘local_recyclebin’ plugin into core” – has passed all the tests and marked as resolved, and is ready to appear in the Moodle core from Moodle 3.1
Earlier recycle bin functionality was available for Moodle through the Recycle Bin plugin which requires a core hack for recycling course modules. However, after integration of Recycle bin in Moodle core, Moodle will also have this basic feature which other LMS have it a long time ago.
You can also test the functionality of the Recycle bin by following the steps mentioned in the tracker testing instructions here.
We congratulate Moodle Users Association for successfully completing its first Project and best wishes for future projects.