Me. I have a smart phone but no data on a prepaid $0.10 per minute and limited text plan. I used Mapmyride for 2 years and last year switched to RidewithGPS. They record no problems and upload the ride when I get home and connect to my WIFI. Obviously you won't have a map to watch if you don't have a data connection.

I've used in the beginning Strava, Endomondo (sp?) My Tracks, and another one. All work just fine tracking your route and uploading after you get home to your WIFI.

If you are looking for a map to follow for navigation, there are a few offline GPS apps. I am using Sygic and just used it to navigate all over Pittsburgh going here and there. I paid something for it, I just don't remember if it was for better map downloads or to enable the turn by turn direction. I tried I think Navmii but didn't like it. I just downloaded OSMAnd which uses Open Street Map. This one is completely free. I haven't tried to use it yet.