select the object, and click the “-” sign in the material tab. this will remove the texture from that object, but not from your blend file.
if a material is not assigned to any objects, it will get a “0” in front of its name, witch means it will be deleted the next time you close blender.
if you click the F button, you will force blender to keep it, even though you restart blender, and the material is not assigned to any objects.
i dont know if you can delete a material, but if you delete the object that its assigned to, or remove the material from every object that its assigned to, save the blend file and restart it, then it will go away.