At church or synagogue
Sit him on your lap from time to time and whisper, "Put your thumb on top of mine," to give him something to concentrate on.
At the grocery store
Make him his own "list" -- index cards with glued-on picture labels from products you buy regularly -- so that he can keep an eye out for those items.
At the doctor's office
Softly clap out a rhythm and see whether he can imitate it by patting his leg.
At the hairdresser's
Bring along a doll or stuffed animal and a comb or brush so he can groom his small friend while sitting in the chair. When you need him to look down, ask him questions like "What color socks are you wearing?" and "Do your shoes have ties or buckles?"
On long car trips
When playing I Spy and singing songs get old, pull things (such as magnetic toys and paper and crayons) -- one at a time -- from your "surprise bag."
In the dentist's chair
Let him hold a small mirror with a handle so he can see what's going on. And give him a pair of kiddie sunglasses -- they'll make him feel cool and keep the overhead light out of his eyes. You can also ask whether he can sit on your lap during the exam.
The biggest problem with getting a toddler to sit still is usually parents' expectations, so keep in mind that your squirmy wormy's behavior is completely normal. A minor attitude adjustment on your part might make life happier for everyone.