I use a navigation app on an Android phone (Galaxy S2), and previously I had a navigation app on a Windows Mobile phone. Never used the data connection - today's smartphones ALL have a GPS chip, and in a pinch some of them estimate the location according to the nearest cell towers (but use pre-downloaded maps)
The app I use (but I stay on the road
) is "Map Factor Navigator" - a professional GPS app, not some half baked amateur programmer's project (and with this I don't intend to bash or criticize amateur/open source software, but unfortunately most such projects never reach their full potential for various reasons). This app uses free maps derived from the Open Street Maps project, and if you buy the full version it uses maps from Tele Atlas (the same used by Tomtom). I've always found the free version satisfactory for my needs.
IMHO the only advantage that dedicated GPS units have is that they are normally very rugged and designed for outdoors use. Put a smartphone in a good case and you're covered for most applications.