I would leave them on the vine until impending frost. This way they don't dehydrate. They should be picked before frost so they don't get frost bitten. You can store them in a shed or any dry area. They keep quite well at room temperature.
Edit to add:
When you pick your pumpkins take care to leave the stem on them. Cut the vine rather than trying to just pull it off. If the stem comes off it seems that they are prone to start rotting at the stem site.
Last edited by jal_ut
on Mon Sep 14, 2009 2:08 pm, edited 1 time in total.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-