Johan The Dog is a free quadruped rig for Maya for use in non-commercial projects.
Grey Matter Gary is a free Maya rig from Squiggly Rigs
The AZRI Rig is a simple animation rig for Maya 2018 and above, representative of video game projects aimed at retaining a high frame rate when working even on lower-end machines. Featured in the book, ‘Game Anim’
Fantasy Crocodile Rig is a free Maya rig that has a super appealing design.
Rocket Girl Rig is a free Maya rig from the VMComix animation blog.
Jasmine Rig is a free rig for Maya that has a load of great features!
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