The easiest art projects to recycle are drawings. Crayon, water paint or ink on paper can all be easily recycled at the end of the day without any kind of special consideration. Collages -- conglomerations of magazine, paper and other supplies -- can also be easily recycled as well as a useful way to use up old magazines or newspapers.
With a little creativity, you can teach your students to make a recyclable paper-based puppet. Using a paper lunch bag, a paper towel roll, some newspaper, and only a few non-recyclables like an elastic band and tinfoil, you can make a puppet that can easily be recycled. Simply fill the paper bag with crumpled newspaper, insert and attach the paper towel roll with an elastic to create a handle, and shred newspaper to glue on as hair. Use tinfoil or colored paper for eyes and draw the rest of the features on the bag itself.
A more complicated project that requires a little disassembling before recycling is a wheelbarrow flower pot. Have your students cut wheels out of cardboard and paint them as desired. Attach the wheels to a laundry detergent scoop with glue or wooden dowels and fill the scoop with soil. The children can then plant seeds and watch their plant grow through the season in their miniature wheelbarrow. Have the students paint the plastic detergent scoop. When finished, dump the soil outside, take off the wheels, and put the plastic and cardboard into the appropriate recycling bins.
Sometimes it's just as beneficial to use old materials that might otherwise be thrown out as it is to recycle a finished project. Plastic detergent bottles can be painted and made into dog food scoops by cutting off the top. Individual cups from old plastic egg cartons can be made into bugs with a little paint and the addition of a head and wings. Even tin cans can be filled with soil and made into small pots for common herbs.