OffMaps is the best global offline mapping app that I have found.

For the UK there is UK Map, which uses the Ordnance Survey data and is therefore better than the OSM data. You still have to select areas to download on the phone though (not limited on download size).

That of course is UK only.

For the rest of Europe I also have TomTom, though of course that only gives you road mapping.

As I say OffMaps is the best global one I've found, though it has been a few months since I trawled the app store looking for alternatives.

Any likely alternatives are highly likely to be OSM based anyway.