Built By Colossus Rigs are free and paid Maya rigs available for download. Founded and run by Roman Jeffery.
Grease Pencil Rigs are a free set of basic rigs for Blender 2.8 that are for use with Grease Pencil. They are aimed to ease the drawing of characters by showing construction lines which you can use for reference while drawing.
Red Dragon Rig is a free Maya rig made by junior rigger, Elise Mathez
Tri Vital has created a collection of awesome Maya rigs and put them on gumroad for free!
Thinking Animation has a great section on the pros and cons of different rigs. As well as a bunch of other resources and tips across the site.
The External World Rigs are a free set of rigs for 65 characters created by David O’Reilly
The Hekaton Rig is a free Maya rig available on gumroad from Luis Perez and Tre Vital
The Mery Rig is a Free Rig project by José Manuel García Alvarez and Antonio Méndez Lora and works with Maya 2013+