On Android at least, the Google maps app lets you download large map areas for offline use, including turn by turn directions. I use this for when I head up into the mountains to explore a new area where the cell service is spotty and it's really convenient. It's a nice complement to a topo map and it means you don't have to carry a separate GPS receiver.

It depends on where you are. The quality of the worldwide online maps by Google and Microsoft varies widely between countries.

I live in Montenegro. Over here, Google and Bing maps aren’t exceptionally good. Some third-party ones are much better. Personally, I own Garmin’s Navigon for windows phone. I’ve heard 4geo.me is also good.

There are topographical map apps that are handy, so that you can use your phone as a GPS unit in the outdoors. Obviously you don't want to rely on them entirely for navigation, but it's a nice supplement to the map and compass, and a lot cheaper than buying a dedicated GPS unit.

Other than that, Google maps does everything I want it to do, with the one exception that I can't pin arbitrary locations. I really want to be able to pin locations, the best I can do is send the location to someone else, but I can't just save it on my phone.