My favorite is OsmAnd+, which is a full featured app that uses OSM and has a plugin to do GPS recording. It can also show you where you have been on an offline OSM map, so it is great for Mapillary.
Free version: https://play.google.com/store/apps/details?id=net.osmand
Pay version: https://play.google.com/store/apps/details?id=net.osmand.plus
Github: GitHub - osmandapp/OsmAnd: OsmAnd
Pay version supports the open source development of the app.
GPS Logger (https://play.google.com/store/apps/details?id=com.mendhak.gpslogger) is easy to use and more light weight. Unfortunately it does not filter bad GPS positions, so you will have to do that afterwards. If you do not filter these, you may see crazy moves like on the map of Mapillary .
Easy GPS Logger is also light weight, but I have lost a GPS track twice. When I press save it have just failed to write it and left an empty file. It does a good job of filtering bad points.
Open GPS Tracker is nice too. Stable and filters bad points, but it takes a lot of presses to end and export the track. It will also show you your track, but dispite called “open” it uses Googles map.
All in all: OsmAnd (or the paied version +) is stable, fast, uses open data, works offline. It takes a bit of setup and getting used to, but you can navigate anywhere in the World without any data connection.