HuMap is a free offline map application that won the Invitel InnoApps Award in 2013. Maps of Hungary (80MB), Budapest (10MB) and other European cities are available. The maps have to be downloaded separately, either from within the app, or manually from the http://humap.uw.hu/ website.

OpenStreetMap (the map source of HuMap) is community-driven like Wikipedia.

✶ Maps are stored on your phone - no internet connection needed while navigating!
✶ Compact, OpenStreetMap-based vector maps
✶ Searchable maps - find any town, street, sight, shop, etc. easily
✶ Nearby places
✶ GPS location feature
✶ Route planning (this feature needs internet connection, there is no turn-by-turn navigation)
✶ Elevation lines and hiking paths (Hungary and Budapest only)
✶ Adding custom overlays
✶ Guidebook (text only, no images)
✶ No ads!

Maps: Hungary, Budapest, Barcelona, Bruxelles, Gdańsk, Hamburg, Helsinki, Kraków, Lyon, Marseille, Oslo, Praha, Riga, Sofia, Stockholm, Warszawa, Wien, Wrocław

I hope you will like this app! Thank you for downloading!

Notes:
1) The maps might not correspond to reality at some places. Never use HuMap when human lives, property or other valueable things may be at stake. Always comply with the local highway code.
2) This app is open source (GNU GPL v3). See http://www.gnu.org/licenses/gpl-3.0.txt. Source code and license are in the assets/ subfolder in the .apk package.
3) The app is compatible with .map files in Mapsforge format. You may use your own maps by manually copying the .map file to /HuMap/maps on your SD card.