Do you place a standing rib roast on a rack or directly in the roasting pan?

Either way save your drippings for Yorkshire puddings. They are worth the effort.

"Standing Rib", to me, implies Bone-in!
If so, sear the outside surfaces and no rack. The bones act as a rack and this helps impart flavor for your gravy/sauce.

I would use a rack...

Also check out http://food52.com/recipes/15387-ann-seranne-s-rib-roast-of-beef. Super easy and delicious!

just as you would use a rack for a turkey, would be advisable to also use a rack for a rib roast so as to keep portion of the roast from cooking in the juices of the gravy at a different temperature from the rest of the roast. also, roast standing in the juice, will absorb more of the liquid, than other parts of the meet. Hope this helps. Happy Holidays!