pickadate.js (GitHub: amsul / pickadate.js, License: MIT) by Amsul is a date picker that works with type="date" or regular text fields, supports various types of date formatting options, and is easy to theme.
The pickadate.js documentation explains how to use and configure the plugin. Basic usage is just $('.datepicker').datepicker(), given a suitable form field.
jQuery Interdependencies (GitHub: miohtama / jquery-interdependencies, License: MIT) by Mikko Ohtamaa is a plugin for expressing relationships between form fields. Rule sets can be created that relate the value of a field to the presence of another field. The simplest example of this would be selecting "Other", and then filling out a value in a text field.