Nokia's Ovi Maps works with pre-loaded maps and can work entirely off-line. You get them pre-loaded with the phone these days or you can download them via a PC. Navigation and maps are free now with the newer phones.
Don't need a data connection, although you do for A-GPS which helps get a better lock especially in built up areas. Small amount of data used, but it's data nevertheless. Can turn off A-GPS though, and also use an external bluetooth GPS for better reception.
With the newer versions of Ovi Maps, it knows about speed limits and if you have a data connection you get traffic info I think (possibly speed traps too but not tested that).
iPhone I'm not sure stores anything on the phone, and the A-GPS situation would still apply.
The best Sat Nav I've used is the one built into my Civic though

. Massive display and the antenna is built into the frame of the car and never had a single problem with signal lock even in built up areas. It gets a perfect position every time. Voice controlled and the map data is pretty good at knowing what is a road and what is a dirt track, and about dead ends etc. It even knows what lane I should be in on approach to a junction.
Downside is the data is all on DVD. The only live data is traffic info and that only applies to motorways and major A roads. Updated DVDs cost £200+ ! The DVDs cover all of Europe though.
Like all sat navs, it still gets things wrong sometimes. Mainly where sometimes a junction is just seen as a bend in the road so it doesn't warn you to turn off. Maybe it's out of date data, though it's 2008 data and the few times it's done this has been on roads that haven't changed in the last 5 years.