Skeletal muscle without antagonist
I would argue that the orbiculares do have antagonists. To some extent, levator palpebrae superiorus antagonizes orbicularis oculi, and zygomaticus major/minor as well as risorius antagonize orbicularis oris.

I can think of three muscle that don't have obvious antagonists:


Stapedius
Tensor tympani
Articularis genu


1 and 2 essentially perform the same action, to dampen sounds reaching the cochlea. 3 elevates the suprapatellar bursa.