Official Resources
GitHub repo - Main repository.
Main Website - Main website.
Core Plugins - Plugins written by core developers.
Forum - Support Forums hosted by osTicket.
Documentation - Official documentation site
FAQ - Technical requirements etc.

Download/Install files
Core Software - download the current stable or maintenance releases

Translations/Language-Packs
Download into /include/il8n folder

Official List - Select "language packs" for latest.
Join the efforts - Help us translate osTicket for everyone.

Plugins
Install into /include/plugins folder

Core Plugins
Developed by osTicket core developers
Authentication :: LDAP and Active Directory - Allows use of LDAP server for authentication.
Authentication :: HTTP Pass-Through - Allows the use of webserver/passthrough authentication.
Storage :: Attachments in Amazon S3 - Allows attachments to be stored in AWS's S3 instead of the database.
Storage :: Attachments on the Filesystem - Allows attachments to be stored on the webserver's filesystem instead of the database.

Beta Plugins by osTicket core developers
unreleased plugins that you have to download and build yourself
Authentication :: CAS - Allows use of Client Access Server for authentication.
Authentication :: Oauth - Allows use of an oauth service for authentication.

Community Plugins
Modifies how the software works, without changing it
Activity Stream - Paid Activity Stream plugin
adSync - Paid Active Directory Synchronization, is a plugin for osTicket 1.10+ which allows the system to synchronize your Active Directory users into osTicket.
Archiver - Archives tickets before delete, and allows for auto-pruning of old tickets.Attachment Preview - Allows files attached to tickets to be embedded in the thread.
Autocloser - Automatically closes open tickets.
Fetch Note - Automatically fetch additional note content on ticket creation.
Field Radio Buttons - Enables the use of HTML form element Radio Buttons.
Mentioner - Finds Staff mentions in a thread and add's them as collaborators to the ticket.
Multi LDAP Auth - Plugin for multiple LDAP servers authentication and LDAP Sync.
notifyReject - Notifies users that your email has been rejected and they need to register an account first.
Prevent Autoscroll - Stops the agent view from scrolling down to the last message in the thread.
Reporting - Paid plugin for extensive reporting.
Rewriter - An osTicket plugin to rewrite incoming emails.

Third Party Integration Plugins
Chrome Extension: osTicket Checker - Checks for new tickets.
Jasper Reports - A Jasper Reports plugin for osTicket 1.9.
Magento Contact Integration - Plugin for Magento to send contact form details to osTicket via the API.
OpenID for Microsoft - An osTicket plugin to enable authentication with Microsoft accounts.
Trello - Integrates Trello with osTicket.
Slack - Sends notifications of new and updated tickets to a Slack channel.