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There is Map With Me [1] that was recommended previously. I bought the Pro version and it's very fast (maps are downloaded and cached in the device), but no directions.

[1] Lite version to try: https://itunes.apple.com/us/app/id431183278

I only know of android apps, but all of the backend services are available and should be pretty easy to splice together for someone looking for an interesting open source project to hack on. I am swamped at the moment, but would be happy to guide someone motivated through the process (I work quite a bit with traffic and routing algorithms optimized for the web).

Skobbler uses OpenStreetMap data for some time in their offline map and navigation apps [1]. They charge a small amount per region download for offline use. I haven't used it for some time but recommended it to a friend who likes it.

A bug tracker for OSM data also exists [2].

[1]: http://www.skobbler.us/info-contact/company-team [2]: http://www.skobbler.us/mapdust