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OsmAnd+ for Android [link] and also for iOS [link] are tracking-free to my best knowledge, of course, what Google or Apple does it unknown.
I have used OsmAnd which uses open street map and allows you to download maps for different parts of the world. Downloads are limited in the free version IIRC but I got the New Zealand map without paying.
Open Street Map based App, support offline navigation. I'm using it for hiking and car navigation, on and offroad. You can even navigate along a imported gpx track
If you don't want/can't use Google Maps, or any other online map service, you can also use OsmAnd which allows for offline storage of OpenStreet maps.
OsmAnd~ (free) or OsmAnd+ (same app, $9 for the convenience of installing it from Google Play).
Open-source OFFLINE maps, navigation, points of interest, Wikipedia POI, hill shading, contour lines, wikivoyage.
I've used Maps.me, but I've never had much love for it. I've not touched it since discovering OsmAnd~.