OsmAnd is a favorite of mine. If you live in one of the covered areas (North America for sure) OpenSuperMaps merges a US style address search and most street addresses into the maps.
OsmAnd search goes by town, street, number while these maps work with “25 oak street Chicago Illinois”. Also, the open street maps rely on croud sharing for map details, so many areas have very little detail, while others put Google Maps to shame.
For navigation, I like Magic Earth. It includes similar search ability and has Waze-like features. The only problem is a lack of critical mass of users to get good traffic and hazard warnings. You can be one more user to supply such info.
@MasterBuilder @HughJanus
+1 for OsmAnd, although for routing, I find Organic Maps to be a little snappier on the UI and feels more like ordinary routing apps.