How do I disable texture filtering? I have a model that is simple and uses low-resolution textures. I'd like to be able to disable the texture filtering so that the textures look sharp and pixels stand out.

An ideal answer would explain how to do this in not only the regular 3d view, but also in renders and preferably also in texture previews.
For the 3D view go to:


User preferences > System.
Then under the OpenGL sub header, you will find "MipMaps" make sure that box is unchecked.


For Blender-Internal go to:


Texture Buttons.
Image Sampling Panel.
Toggle MIP Map button.


Update

As of blender 2.71 texture nodes now have an option to change the interpolation method:



Using Closest will keep the pixels sharp.



Old Answer

For cycles, this is a needed feature. Here's a workaround (32 is the size of the texture) :