You could tile them. Just cut out the good parts and glue them down.

If you have a variety of colors and styles, maybe something that looks like a patchwork quilt so it doesn’t look so scrappy?

We lined the floor of our kids cubbyhouse with a lino offcut. Much easier to clean out - you can either sweep it or take out the lino and hose it down.

A “carpet tile size” piece is good for going under cat/dog food bowls to keep the floor clean!

cut them into strips and weave doormats from them, the ends can be stapled.

Use the back of the vinyl flooring to paint your own floor cloth. Here is how ; use the back side and paint with a light house paint, then when dry paint the color you want for your background with acrylic paint, then trace your design & paint it with acrylics. Lastly then seal it with multiple coats ( 5 or 6 ) of a good sealer. These will last for years.

I have a long narrow piece of lino rolled up in a cupboard, I use as a pasteboard when Im decorating.

if it’s truly vinyl, i wouldn’t want it anywhere near my compost heap - pvc can leach out toxins.
http://en.wikipedia.org/wiki/Pvc#Health_and_safety

vinyl/linoleum flooring makes good shims, small or large: they are soft enough that they will give a little, but not soft enough to lose their depth in compression. i use them in construction when furring out walls to install new drywall, to build up subflooring, to add depth to shelving/cabinetry, and small pieces make great shims behind door hinges.

I am one of those people lucky enough to have a second home with a small cottage on a lake. What I usually end up doing is recycling all my old furniture and salvageable goods from my regular house into there. An example is I recently took the vinyl flooring out of my kitchen in my regular home and used it as a taped down floor in my utility room in my cottage.

Cut it to fit cupboards under your kitchen and bathroom sinks.

Use as insoles for shoes