Since several people have come up with their own ideas for iPhone copy and paste, I thought I'd throw mine in.
The challenge is to come up with something both intuitive and quick. The best solution I've come up with so far is simple. It is basically the caret positioning method, but expanded slightly. To position a caret, one simply presses and holds where they want to position the caret, and after a little magnifying glass (meant to aid them) comes up, "corrects" by moving around their finger.
My text selection idea is nearly identical. One selects a starting position like normal, and then does the same thing for the ending position, but instead of simply pressing down and holding, he or she double-taps and then does not release. This would tell the iPhone not to erase the previous point, but use it as a starting selection point.
To copy or cut, simply tap the selection itself (much like one taps a link), and a command window (including cut, copy, paste, share) should pop up.
Simple, easy, quick.
Pasting shouldn't be too hard either. Perhaps simply position the cursor, and then tap, and an "insert" window could pop up. This window would include paste, insert picture, etc.