GPS Tracklog from iPhone
I use "GPS Kit" for this. It lets you record the movement of your iPhone for as long you want, and save them for later viewing. It even lets you broadcast your track so that others can view it as you move, if you want to do that for some reason. You can also cache offline maps, if you do want to be able to see where you are in remote locations. It doesn't need the maps to function though. It tracks your GPS coordinates the entire time, you just can't see where you are without data, but it sounds like that's okay with you.