As you may have seen on my brief iPhone 4 review, I ran into a little problem with the iPhone's camera shutter not opening. After a lot of investigation, I tried several methods to try and remedy the problem; I would recommend trying these steps (in order) if you run into the same issue:
[update]Commenter Gillian found a workaround (below). If this works for you, then it is probably a software problem and will probably be corrected in 4.1.
If this works for you, then it is definitely a software problem, and will probably be fixed in 4.1.
If none of these solve your problem, you are most likely out of luck (which is what happened to me). Time to call Apple (1-800-MY-APPLE).
A few tips, though:
They will probably give you two or three options to choose from:
Setup an appointment at your nearest Apple Store, then go in for an exchange.
Have Apple send you a new iPhone first, then you send your iPhone back in the same box. There is a catch to this one, however. If you do not have Apple Care, there is a $29.99 shipping and handling fee. If you do have Apple Care, there is no fee. In both cases, you will have a $599 hold on your credit card until they get the old device back.
If you are in a situation similar to me, where you don't have an Apple Store close by, can't be without the phone for a few days (e.g. you need it for work), and don't have the money to purchase Apple Care or pay to have the unit shipped, there is a possible solution: ask for the call to be elevated to a higher-level Apple Support Representative. They can often waive any fees (you'll still need the hold on your card, though), and your phone will probably be to you within a few days.
Good luck, and I hope this helps.