Puppet Shows

A very old form of spectacle, Puppet Shows use some kind of puppetry to feature their characters in real-time (setting it apart from animation, including Puppet Stop Motion). Mostly seen within children's entertainment, but also used for satirical parodies, with puppets caricaturing real-life people.

There are two main categories of such shows:

Hand Puppets, the most well-known being Jim Henson's The Muppets.
Marionettes, mostly using Supermarionation. Usually features down-to-scale decors.

Other possible types include:

Animatronic puppets, a modern development of Muppets.
People in Rubber Suits, a.k.a. Suitmation, which can appear alongside either type (on the same scale with hand puppets, or as giants with marionettes).

An otherwise human-centric show using a few puppet characters doesn't belong here. However, some Puppet Shows, while using mainly hand puppets or animatronics, may also involve some human characters and thus tread the line. Marionettes shows can also make use of live animals to figure monsters.

Examples of Puppet Shows include:

Animatronic Puppets

Films

The Dark Crystal
Labyrinth (really only had three human characters for most of the movie)
Teenage Mutant Ninja Turtles (largely live-action, but the main characters are these)