OpenStreetMap

Websites: OpenStreetMap uMap (customised maps) OpenRouteService (customised routes)
Android apps: OsmAnd~ (F-Droid) OsmAnd (Google Play Store) Organic Maps (F-Droid) Organic Maps (Google Play Store) and others
iOS apps: OsmAnd Organic Maps and others

OpenStreetMap (OSM) is a huge collaborative map database that anyone can use and edit (sort of like the Wikipedia of the map world). OpenStreetMap is sponsored by various universities and other organisations, and does not track its users.