In Blender, a texture has 2 components: A) the texture image file itself and B) the texture data block. A texture can assigned to one, multiple, or zero texture data blocks. If it's assigned to zero data blocks, the texture file's association with the .blend file will be removed upon saving.
If you want to remove the texture file itself, the best place to do this is the UV/Image Editor. At the bottom, click on the source field and you'll see a list of all texture files associated with the .blend:
Select the texture file you want to remove and click the X:
Understand that this will leave behind any texture data block that the image was assigned to. To remove texture data blocks, select the desired block and click the X in the texture properties panel:
