The Morpheus Rig is a free Maya rig created by Josh Burton available to download from his personal website
Morpheus Rig v1.0 (FREE)
Minion Rig (FREE)
The Minion Rig is a free Maya rig based on the popular Minion characters from ‘Despicable Me’
Pink Panther Rig (FREE)
The Pink Panther Rig is a free character rig for Maya based on the popular character ‘Pink Panther’
Ultimate Rigs (FREE)
The Ultimate Rigs are great free Maya rigs for practicing body mechanics
Animation Buffet
Animation Buffet is a great resource for free Rigs and is constantly updated by Jean-Denis Haas (ILM)
Tiger Rig (FREE)
The Tiger Rig is a free rig compatible with Maya 2015+
Josh Sobel Rigs (FREE+)
Josh Sobel has some great affordable rigs (his Kayla rig is especially great). You can also get his Bonnie rig for free!
Longwinter Rigs ($10/month)
Longwinter Studios are offering access to their whole rig collection (30+) for only $10 a month. Not too shabby!
Malcolm 2.0 Rig (FREE)
Malcolm 2.0 Rig – A great free rig from AnimSchool
Animator's Resource Kit 