Drag’n Drop Calendar With jQuery: FullCalendar
FullCalendar is a jQuery plugin for creating a full-sized calendar with drag’n drop support that can fetch events via Ajax requests on-the-fly.
It can be easily configured to use your own feed format (an extension is provided for Google Calendar).
The plugin does not come bundled with features like "changing an event’s name or time" but has hooks for user-triggered events that makes it possible to add such features.
The calendar’s look/feel can be customized via CSS & it is well-documented.