A couple of people have mentioned Wizball, but I think Sensible Software's sequel, Wizkid, is actually stranger. I copied the plot synopsis from Wikipedia:
"The story starts after the Wiz and his cat Nifta had restored colours to their world. They were both married (to different spouses, apparently) and had children: the Wiz had a son, Wizkid, and Nifta had eight kittens. All was peaceful and happy until the evil mouse wizard Zark came and kidnapped the Wiz, Nifta, and all the kittens, imprisoning them in different parts of the world. It is Wizkid's job to save them."
A practically Shakespearean tale, then.
Before that there was a game on the Amiga (and Amstrad and Spectrum) called Chubby Gristle. I won't bother trying to describe it, but... well, it was a bit like Jet Set Willy but even weirder.
"The story starts after the Wiz and his cat Nifta had restored colours to their world. They were both married (to different spouses, apparently) and had children: the Wiz had a son, Wizkid, and Nifta had eight kittens. All was peaceful and happy until the evil mouse wizard Zark came and kidnapped the Wiz, Nifta, and all the kittens, imprisoning them in different parts of the world. It is Wizkid's job to save them."
A practically Shakespearean tale, then.
Before that there was a game on the Amiga (and Amstrad and Spectrum) called Chubby Gristle. I won't bother trying to describe it, but... well, it was a bit like Jet Set Willy but even weirder.