In case you hadn't already heard, you can no longer buy an iPhone at an Apple store with cash. You have to pay with a credit or debit card, and you are limited to purchasing two. In fact, you can't even use your Apple gift cards, even if they were purchased with a credit card. Apparently, Apple doesn't approve of the thousands of iPhones that have been purchased, unlocked, and resold. Go figure. Not accepting good ol' US greenbacks seems like a dicey stance to take from a legal perspective, but according to Bryan Gardiner over at Wired's blog network, it's completely legal. The law that brings this practice into question is Section 31 U.S.C. 5103, which states:
United States coins and currency (including Federal reserve notes and circulating notes of Federal reserve banks and national banks) are legal tender for all debts, public charges, taxes, and dues.
However, this seems only to apply to money owed to creditors, not for the sale of goods or services. So Apple seems to have a leg to stand on here. However, I still expect that they'll get sued anyway.
If you still want to buy an iPhone without leaving a paper trail, though, I suppose you could buy yourself an American
Express gift card. It can be used just like a regular Amex card, and Apple takes Amex.