Reclare is a lightweight library to manage the application state alongside business logic. It is inspired by Redux and the Elm architecture.
FullCalendar is a full-sized drag & drop event calendar (jQuery plugin). Excellent for Outlook-style calendar-style event and booking systems.
Moment.js is currently the de facto library for handling and manipulating dates and times. Comprehensive and probably used in all major projects requiring datetime manipulation. Supports dozens of local time formats. Works in browser and with NodeJS.