I've written before about navigating with the iPhone, and the differences between having the maps on board your phone versus downloading them over the air.
The differences were readily obvious on my recent photo trek to the Monument Valley area on the Arizona and Utah border. About 30 miles south of Kayenta, I fired up the Garmin GPS app. It needs an internet connection to work, and none were available. In that part of the country, AT&T has nothing, so when I had any signal at all, I was roaming. You can see the result in the gallery -- a blank screen with a car icon (not much help). No maps, no destination information, nothing. I then fired up my Navigon app, and even though there was no voice or data service, I had a detailed map because the map info was on the phone. Apps like Navigon still use the internet for some services, like traffic or Google for newer destination searches, but for getting from place to place, the app was full-featured.
Of course, if you don't venture out of the cities or good coverage areas, almost any nav app is fine, including the ones that require maps to be downloaded in real time over the air. However, if you get off the beaten path, you simply can't depend on an app that has no pre-installed maps on your phone. Be sure to check the descriptions in the App Store about where the map data is coming from. There are plenty of apps that use both methods, and there is a wide choice of features and costs. Just don't get caught with a blank screen if you have spent good money on a nav app for your iPhone. Note: One of our readers quite rightly points out that if you can set the route while you have connectivity some of the over the air apps can cache the trip. While that is true, without connectivity when you plan the route, you will get a blank screen, as demonstrated in my real world test.