Minecraft is a Game involving a 3D world of blocks. Blocks form landscapes of land, sea, rock, trees etc which can be generated randomly or designed externally and/or shaped within the game. OpenStreetMap map data could be used to generate a world, as a "converter".
Probably the only implementation of this idea so far is Christopher Gutteridges Minecraft Ventnor:
Minecraft Ventnor & Newport
Minecraft Ventnor: http://ventnor.totl.net/
Christopher Gutteridge describes how he spent countless hours making a 3D model of Ventor (a place in the Isle of white) by placing blocks in game (battling zombies at night time all the while!) He did use OpenStreetMap at this stage, for planning, however later went on to create a converter, which took OpenStreetMap data and produced a minecraft map in an automated way. All detailed in the 'making of' section and open source on github
Minecraft Newport: http://users.ecs.soton.ac.uk/cjg/newport/
Now he's back! With Minecraft Newport ^
Mapbox minecraft-like unity demo
Blog post: How to design a Minecraft-inspired world with Mapbox and Unity is a demo of a new Mapbox unity integration. The output is not minecraft, but a similar Voxel landscape. And actually the source data is only a little bit OpenStreetMap ("giving distinct colors to grass, wood, water"). It's mostly whichever terrain data mapbox brings in.
Ordnance Survey terrain data
minecraft fun is an area where Ordnance Survey have pipped us to the post. Ordnance Survey Terrain data has been converted to minecraft, as a hack someone did at one of their events, and they frequently use this as a flagship example of the kind of interesting unexpected outputs you get from open data.
It's worth noting that conversion of terrain data to minecraft is a more obvious option really, since it works at any "zoomed" out scale factor you might choose (How high should a 1000 metre high mountain be measured in blocks within minecraft?) OpenStreetMap doesn't have terrain data directly. Any relief maps with OpenStreetMap are built by bringing in 3rd party terrain datasets (of which this Ordnance Survey data is one option in fact). To convert OpenStreetMap to minecraft you're really looking just at 3D buildings data, for which the scale factor needs to be quite "zoomed in" (How high should a 3 storey building be measured in blocks within minecraft?)