Sure, you can use more or less any tile source where provider has allowed it (which excludes Google).
mapView.getLayers().setBaseLayer(new TMSMapLayer(new EPSG3857(), 0, 18, 6,
"http://a.tile.opencyclemap.org/cycle/", "/", ".png"));
This is added now to Nutiteq Tile sources Wiki page also
For MBTiles you should use the MBTilesMapLayer.java from AdvancedMap3D project. This is up-to-date code and for most of the data source layers we keep open source code there, so you can tweak it for your needs.