For general map browsing, I tend to use Organic Maps. It does a better job rendering urban environments, and even shows primitive 3D buildings when OSM has the data. It's decent as a driving GPS.
Debatably, the best OSM-powered mobile app is OsmAnd, which is a more powerful application with the downsides that come with that -- slow, lots of settings, crowded UI. The killer features IMO are: 1) it's the only one (best I know) that allows users to zoom extremely close, which is vital to see all POIs in dense areas and also helpful to see details of parks and trails 2) it's the only one (best I know) that can interface with Android Auto enabled vehicles. (There's an iOS version of OsmAnd but I've never used it since it requires a subscription for map updates.)
There are particular use cases (eg hiking) when one of these OSM-powered apps will be an adequate or even superior replacement for Google Maps. These use cases are the exception. Google Maps has its own two killer features: 1) realtime traffic for car navigation 2) sophisticated public transit routing, again with realtime data integration.
All 3 of the above apps will attempt public transit routing, but I'd never use them. They don't comprehend train schedules, much less realtime data. They don't handle bus directions at all, though this might be down to the state of the OSM data in the locations I've tried them -- bus route relations are difficult to create and maintain in OSM, and easy to break.
I'm an OSM fanatic myself, so it's saddening not to be able to wholeheartedly endorse any of the current slate of apps. The good news is that the available apps have never been better and continue to improve. Sometime soonish it might be merely a minor inconvenience to de-google your mapping life. (Apple Maps is also pretty good with realtime traffic and public transit routing, if that's an option.)
Sadly, since OsmAnd+ 4.1.x it requires Android 6+ to work.
Looking inside changelog of OsmAnd+ I really can't understand why Android 5.x support was dropped.
Actually I can't decide where to move next after OsmAnd: Organic Maps[1], Pocket Maps[2] or something else.
Also from-time-to-time tested Navit[3], but its GUI is far away from what I'm looking for.
[0] https://apt.izzysoft.de/fdroid/index/apk/net.osmand.plus?rep...
[1] https://apt.izzysoft.de/fdroid/index/apk/app.organicmaps?rep...
[2] https://apt.izzysoft.de/fdroid/index/apk/com.junjunguo.pocke...
[3] https://apt.izzysoft.de/fdroid/index/apk/org.navitproject.na...
I mean, that's a pretty old version of Android.
It might have something to do with the requirements for the Android Auto integration, which was just added recently.
Have been using it for six years now.
Search is good enough.
I don't know if there is an alternative.