When I was little, I had a pet mouse. (singular)
When I was little, I had pet mice. (plural)
I fear mice. (In general, no matter what the mouse looks like or it's size).
I fear the mouse. (a mouse specifically, other mice wouldn't bother you).
Do you have mice?(usually as in a PEST problem)
Do you have a mouse? (usually as a PET)
Many ways of using it, but singular and plural are the basis of the word. Other animals have a plural that changes like this.