At that level, a fax is just data going from one point to another. A fax machine or a computer is needed to convert the fax to something that can be read. Just like any other form of data.
The original poster should also be aware of pc cards for laptops, which will handle the data transmission over cell towers. Available from your friendly local cell phone carrier.

If you use your cell phone to connect to the Internet for a laptop or PC, you should be able to receive faxes if your computer is compatible. I think that’s what your asking, cell phones by themselves do not receive faxes.

As far as I know there's no such thing as a fax machine cell phone. You can get faxes on the Internet though with a fee. Go to eFax - Email Fax Services. There might be others but that is the original company that started it out.

I am looking at dumping my landline phones and be all cell. If I do, how can I use a fax machine? Is there some way I can use a fax machine with a cellphone and which cell phones?