Animbot is an essential free Maya toolset for animators made by Alan Camilo. Highly recommended!
AnimSelector is a free and super simple Maya script that allows you to quickly setup selection groups that you can later pickup from a GUI or assign to hotkeys.
Keyframe MP is is a compact, yet powerful, media player designed to meet the needs of animators. Features include scrubbing (with audio), single frame stepping, an adjustable playback range and bookmarks. Free Trial available.
Graph Editor Redux is a redesign of Maya’s curve editor toolset. Not only does it reorganize the classic graph editor functions, it provides new tools that many animators have found extremely helpful in massaging animation performances.
Mixamo Auto-Rigger is a free online tool that allows you to upload any 3D human model with two arms and two legs and get it rigged with a full skeleton and skinning weights.
Cg Monks Toolbox is a free toolset for Maya that includes a large selection of handy animation and rigging tools
Morgan Loomis has a bunch of great animation tools and scripts for Maya on his website free to download. You can download the full animation shelf or get them individually!
Animschool Picker – A great free control picker for Maya by AnimSchool
aTools is the ultimate free utilities belt for Maya animators.