Is it possible to record video of the iPhone screen, and if so how? I'm talking about video screen capturing, not using a camcorder or any app that requires jailbreaking my phone.
Don't overlook the power of running things in the iOS simulator. Xcode is free for Lion users. This is a very limited solution since you aren't really on the iPhone and you can't run app store apps, since its running computer versions of the apps, not the ones you download from iTunes.
Being a paid developer allows some extra flexibility in capturing the screen while tethered, but this might be an alternate.
Until this becomes a feature, you'll be stuck with this and the other options you have ruled out - a real camera or jail breaking to modify the code and get a dump of the screen.
As a previous commenter mentioned, video output is an option.
This appears to be available on the newer iOS devices (when loaded with iOS 4.x and later).
Check out this article from Apple about video out for iOS devices. You'll need a VGA adaptor for your device. You'd then be able to feed the video signal into another device that can record the signal.
So, you don't necessarily need to jailbreak to do this.