I use Google Maps. I just try and plan it one leg at a time, so that Google will show me my options. On my iPad, to do a trip with multiple destinations, I use an app called Maps+. It's really just another way to access Google Maps, but I find it more functional for planning some routes.

I also will use GPS Visualizer to take a route in Google Maps and turn it into a file that I can import into MotionX GPS, which is another mapping app I use. MotionX GPS doesn't help me plan routes, but it does help me store them. It also lets me download map data in case I need to access it when I don't have internet access.

Another program I'm fond of on the iPad is Maplets, which lets you download pdf maps that may be available for the area you're traveling in (like most state parks will have a pdf map of the park, and some counties have bicycle maps). If the map presents the data in way that Maplets can work with, Maplets will show your location on the pdf map.

It's always my intention to carry a paper map as a back up, but I don't use it for route planning anymore, and sometimes I forget it entirely.