(Take it from someone who's spent two hours holding his iPhone at an upright angle.)
If you still have your hotel room-key floating around in your pocket, you can pull a Macgyver move and turn it into a solid, stable iPhone stand.
Instructables has the instructions, but there's nothing terribly tricky about this: Just fold the card into the shape shown in the photo.
(This should also work with any similar piece of plastic, such as a used Starbucks card or gift card.)
You may have to fiddle a bit with the folds to get just the right viewing angle, and not all cards will stay in their folded positions.
But in a pinch, this is a perfect way to prop up your phone. And it's a lot sturdier than my previous favorite, the business-card stand. Plus, you get the satisfaction of using that room key for something practical instead of just tossing it into a landfill.
While we're on the subject of iPhone stands: