This summer, I went on vacation to a place that was not covered by OpenStreetMap, so I became a small OpenStreetMap contributer and mapped the surroundings. Here’s the list of software that I used on my Android devices.
To gather GPS data, I used OSM Tracker for Android, available both in Google Play and via F-Droid. It’s a nice GPS tracker with fast Points of Interest (POI) placement shortcuts. It should be able to upload traces directly to OSM, but this functionality always crashed with me; uploading the generated traces (.gpx) with the website worked once I renamed the files to remove non-ASCII characters.
To edit the map, I used Vespucci, which is also available both in Google Play and via F-Droid. It’s fine for relative small edits, but for larger one you’d better use the Flash-based Potlatch 2. Another useful application to edit details such as the name of roads or POIs is OSMapTuner (see update), available in Google Play.
A more comprehensive list can be found on OpenStreetMap’s wiki:
Android software supporting OpenStreetMap.
Update: I’ve just found another editor for POIs, Mapzen POI Collector. It can add POIs and has a much nicer user interface. However, it is limited to the most common types of POI, so if you have very special needs, it’s not for you.