S.,
I am a pre-school teacher for children ages 15 - 24 months so I do have a few ideas.
Empty egg cartons -
can be used to plant seeds
can be painted
cut the ridges apart & the egg carton becomes a caterpillar
Empty plastic milk cartons -
cut out a section of the front, paint and hang as a birdfeeder
Empty cardboard milk cartons -
cut the tops off and make "houses"
leftover popsicle sticks -
fences for toy animals
picture frames
stick puppets - glue cutouts from coloring books to popsicle stick (you will need to reinforce the cutout with light cardboard that you can get from a cereal box, etc)
collages can be made with many household items - for example: cutuout pictures from magazines, food boxes, old clothing cut into small pieces, tissue paper from gifts and gift wrap, junk mail, cotton balls,etc
empty toilet tissue rolls and empty paper towel rolls can be painted, colored and used for many things
empty boxes of various sizes can be decorated to make building blocks
empty water or soda bottles - add solid materials such as rice, dry beans, small pebbles, then use a glue gun to glue the lid on and these become "shaker" bottles
or add water, a drop or two or oil and food coloring - again use a glue gun to secure the lid and these become science experiments
empty spice bottles with the lids with small holes can be used to sprinkle flour, cornmeal, etc over wet paint to create a different look
There are many, many other things. Try doing a Google search for inexpensive children's art projects and I am sure you will find much more.