I work for a textile company and when we have something discontinued or slightly damaged, I contact one of our local schools that have an interiors dept. Preschools are another great place - they might be able to use the samples in an art project.

I know INTERFACE
http://www.interfaceglobal.com/Sustainability/Sustainability-in-Action/Closing-the-Loop.aspx (Flor's parent Company) says in their marketing/Green Statement that they'll pickup/remove old carpeting to recycle when their carpeting is being installed.

You can donate them to your local animal shelter.

Habitat for Humanity operates reStore, a building salvage shop with outlets across the country. If you have a reStore nearby, I'm sure they would love to take your carpeting.

I remember having "carpet squares" in kindergarten since we had a tile floor and our teacher didn't want our bums to get cold sitting on the floor. Also - you can check with local universities - dorm rooms are usually tiled, and it's awesome to have a rug in your room for color and to keep your toes from getting cold in the morning.

If you call the New York Shool of Interior Design they will send someone to pick them up. They use them in the atelier for students to put together design projects. They always appreciate the donations. They are on 70th street on the Eastside between 3rd and Lexinton Avenue.

if these are sample squares, what about donating them to materials for the arts? i think that's the name of the nyc agency that makes these materials available to educators for their students projects.

Preschools and kindergartens use them as part of classroom management - each child gets a carpet sample square to mark out his or her space. Cuts down on the fussing, I guess. I wanted a couple to try out for my own kids at home, and all the places I called said they had waiting lists of preschools for their discontinued carpet samples.

Animal shelters will find them invaluable.

Materials For The Arts
Build It Green
and perhaps
Baltic Bazaar
(they take upholstery remnants from the trade)
http://www.balticstreet.org/balticbazaar/index.htm

There's always FreeCycle
http://www.freecycle.org/

Animal rescues and shelters would LOVE to have carpet remnants, especially those samples that have completed edges. They are particularly useful in cat cages, so if you have any cat specific rescues in the area, they would love them.

habitat for humanity and other organizations have building salvage stores that will take and sell new and used building materials. They typically do not take carpet because it is used, but these are new, so maybe they would take them.