For my Animation Thesis and VFX Master's project, I've spent a lot of time rigging using Advanced Skeleton for Maya. For my thesis in particular, my non-traditional character/animal designs and the variety of different creatures and movement styles I'm employing made it necessary to create some very specialized rigs.
My thesis film's main character, Ranger Dave, is a human figure based largely on silicone stop motion armatures. His rig requires a lot of detail and careful weight painting, as the film requires closeups of his face and hands, as well as a lot of full=body action shots, which run the gamut from very naturalistic to highly stylized and cartoony.
Instead of a typical face, he has only sunglasses, eyebrows, and a mustache, which required a specialized facial rig to be built from scratch to provide the proper level of control.
The primary antagonist, on the other hand, has paper-cut swap out facial features in the style of Robot Chicken. These were created using flat planes parented to the face, and then a control which can swap various textures onto the eyes and mouth respectively.
For the various animal creatures, each one was designed based off of a specific handcraft, and had a distinct set of challenges. For example, the seals are only ever seen in closeup, the seagull mama has wings which unfold like a fan, and the crane has a neck made of glass beads. Thanks to Advanced Skeleton's modular system, things could be adjusted as animation progressed to account for various issues, such as adding squash-and-stretch controllers, adjusting joint placement, or adding additional controls.
For my VFX Master's project, I initially began using a custom rig of Kermit the Frog to model my recreation of Antron Fleece, however, after talking wit the Henson Foundation I was encouraged to create my own Muppet-type character to avoid publication issues. Resultingly, I designed, modeled, and rigged Swimothy, who was designed to replicate as accurately as possible the construction and mechanics behind a Muppet to ensure the most accurate movement possible. For example, the rotation of Swimothy's shoulder is split across two joints, since Muppet arms are attached using a snap, which allows 360 rotation on one axis, and then the plush material of the actual arm deforms to provide rotation on the other axes. Additionally, Swimothy is set up to default to IK controls for the hands and feet, fixed eyes, and a body split into separate parts to provide the most accurate animation possible.