Television and electronic games have all but stopped parents from engaging in some of the older types of activities with their children. One of my greatest joys occurs when I draw a smiling face on my thumb and show it to a toddler. I have not met one who does not want me to draw a face on his thumb. Then, my thumb "looks" at his/her thumb and starts having a conversation. What a great way to teach social interaction! You could even draw them on his/her other fingers so that they can have a play group. One possible secondary benefit to this thumb person is the possible resistance to thumb sucking, because he/she would not want to "eat" the thumb person. Be certain to use nontoxic markers when you draw them.
Drinking straws make really cool musical instruments. You flatten one end. You really have to work at flattening one of those plastic straws, unless the plastic is really thin. Then, cut off the corners to leave a near point (leave a little bit of a straight edge at the front). Continue to work on flattening that tip. Insert the cut end in your mouth so that you lips are on the round part. You may have to work a bit to get the flat part just right. Blow. The shorter the straw, the higher pitch sound you'll produce.
Paper airplanes are a lot of fun. You can have distance contests with them.