I'm writing a Minecraft like static 3d block world in C++ / openGL. I'm working at improving framerates, and so far I've implemented frustum culling using an octree. This helps, but I'm still seeing moderate to bad frame rates. The next step would be to cull cubes that are hidden from the viewpoint by closer cubes. However I haven't been able to find many resources on how to accomplish this.
Answer
Create a render target with a Z-buffer (or "depth buffer") enabled. Then make sure to sort all your opaque objects so they are rendered front to back, i.e. the ones closest to the camera first. Anything using alpha blending still needs to be rendered back to front, AFTER you rendered all your opaque objects.
Another technique is occlusion culling: You can cheaply "dry-render" your geometry and then find out how many pixels failed the depth test. There is occlusion query support in DirectX and OpenGL, although not every GPU can do it.
The downside is that you need a delay between the rendering and fetching the result - depending on the setup (like when using predicated tiling), it may be a full frame. That means that you need to be creative there, like rendering a bounding box that is bigger than the object itself, and dismissing the results after a camera cut.
And one more thing: A more traditional solution (that you can use concurrently with occlusion culling) is a room/portal system, where you define regions as "rooms", connected via "portals". If a portal is not visible from your current room, you can't see the room connected to it. And even it is, you can click your viewport to what's visible through the portal.