For editing, I recommend Vespucci and StreetComplete. I personally much prefer the former, but some people swear by StreetComplete.

For navigation, I recommend OsmAnd or Organic Maps. This is another situation where some people swear by Organic Maps but where I much prefer OsmAnd.

In addition to the ones already mentioned, there is another one for contributing called Every Door

E.g Osmand, organicmaps, magic earth. Magic earth is as far as I know the only one supporting real time traffic (and hence route optimization upon traffic incidents)