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.
Audit Log - Performs audits for User and Agent activity.

Community Plugins
Community plugins are made by the community not the developers. They are not supported or recommended by the Developers and are not affiliated with the Development Team.
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.
Motherload – Paid plugin for rapid plugin development by cartmega.
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.
osBackup Lite – automated local osTicket file and database backups
osBackup Premium – Paid automated osTicket file and database backup with external storage locations
osTicket Alert Plugin - Sends alerts to Users when an Agent assigns their ticket to another Agent or another Agent claims the ticket.
osTicket Google Recaptcha - Plugin adds form type Google Recaptcha
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.
Superlists – Paid plugin for ajax custom lists by cartmega

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.
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.