Even though Sitecore is a proprietary platform there are open source initiatives from Sitecore. What are those?
Sitecore Rocks integrates directly with Microsoft Visual Studio 2013, 2015 and 2017 and gives developers a fast, streamlined development experience by letting them use the tools that they are familiar with.
Dynamics CRM Security Provider is available
Expose CRM contacts as Sitecore users, CRM marketing lists as Sitecore roles and interact directly with Dynamics CRM.
Dynamics CRM Campaign Integration Module
Integrate your CRM system with Sitecore, and enrich the CRM with information about customers' online activity.
SharePoint Connect offers page-level, item-level, and API-level integration. It can be used with Sitecore XP and gives you the tools to harness the advantages of SharePoint's document management features within Sitecore.
Sitecore Instance Manager (SIM)
SIM is an open source tool for managing the local park of Sitecore instances. You can install, locate, maintain, reinstall or delete Sitecore products. It has API and plugin engine so you can extend it for any your need.
Sitecore Diagnostics Tool
A tool that allows to automatically check Sitecore solutions for common problems and configuration errors.
You can also use this repo to file issues.
The blog module for Sitecore. While getting a little long in the tooth, there is a small group of folks maintaining this still, with plans to modernize the architecture.
Sitecore Driver for LINQPad
This product lets you use LINQPad as a lightweight environment to run Sitecore code without deploying that code to your server and without having to create a Visual Studio project.
The driver was originally developed in order to make it easier to troubleshoot Sitecore search queries, but it can be used to work with other Sitecore APIs, too.
Sitecore Commerce Connect Starter Kit
The Sitecore Commerce Connect StarterKit is a sample project showing how to create a custom connector for Commerce Connnect, in this case nopCommerce is used as the External eCommerce System.
An example Sitecore Solution that showcases the Helix architecture principles.
Please note that this is a community wiki. Edit this answer to add more projects DO NOT post another answer.