The right way:
You need to be vary particular about how you set your cube up. I use a cube, each face subdivided into a 16x16 face arrangement; you probably need to manually subdivide for this, rather than use a subdivision surface modifier(15 cuts). Then I setup a bevel modifier with the following settings tweaked: Width: 0.005 Segments: 2 Uncheck "Clamp Overlap"
Next I UV project each face from a dead-on view (Use your numpad to get things lined up) Edit-mode "U" [Project From View(Bounds), OR try Cube Projection from a front-on Iso view (Sometimes works, sometimes doesn't!)
Add a Displacement Modifier. Load your texture (As a note, you will need to touch-up most default Minecraft chips before using them as a texture. EVERYTHING will need it's resolution increased to somewhere around 256x256 without any interpolation, most things will need to be redone from scratch as a black and white height-map, dark is low, light is high.) I reccomend using Stone as a test item, because it involves no processing after you've increased it's resolution.
Use this map, and use UV Texture coordinates for your displacement modifier, play with your Strength and Midlevel to taste.
Almost done, now, add another Bevel modifier: Check Clamp Overlap (On) Limit Method: Angle
As you can probably tell, this produces an INSANE amount of polygons for what we're trying to accomplish. New and improved method:
This method presumes you know how to remove doubles. Select all verticies in an object, "W" [Remove Doubles] It also presumes you are in GLSL viewing mode (3D modeling window's right-hand pane. Tap "N" to bring it up if it's not there. Under "Shading" switch to GLSL mode, then in the 3d window tap "Alt+A" to get into shaded textures mode.
Start: Create a cube. Delete all but one face. Subdivide face into 16x16 faces (15 cuts). UV project from view bounds. Apply that texture in a material, shadless might help. Select the faces you want at a certain height, extrude them upwards Repeat with the next level of faces until complete.
In Object mode, duplicate and rotate that plane until you have a cube again. Edit mode, remove all doubles, then you're going to have to play around to fill in the gaps around the edges and fix clipping.
Add your bevel modifer, limit angle, and adjust to taste.
This method is a bit more work, but produces a significantly lighter poly-count, as well as makes the mesh more managable for adding in, say, ores to a Stone model. Another trick to conserve polys: For the far-off blocks, just apply a displacement map and let it influence Normal or, in cycles, use it as displacement. I hope this helps."