Does Google Navigation work offline? I know that I can download and cache parts of the maps in Google Maps. When offline (e.g., in flight mode, but with GPS enabled) I can explore these parts of the maps.

But when I try to use the Navigation to get directions, it seems it doesn't work offline (even when navigating inside the cache map areas).

So, does the navigation feature always need a connection (either WiFi or 3G)?
Unfortunately, yes. For now, that is how Google has created the Maps application; you cannot use Maps (or Navigation) without internet access. 

There are other apps that exist, though, that allow you to download maps for use offline. Sygic and Navfree, for example, both allow you to store maps on your device and then only require a GPS fix to give you turn-by-turn directions. Note you still need internet (WiFi or data network) to download the maps the first time, but after that, you're free to shut data off.