I posted a link a bit ago where some WikiLeaks supporters were calling for attacks against financial organization FAX machines. Here is the link:
While I hope these sort of attack does not occur, I can say that they could be very disruptive. While there are alternatives to FAXes, they are still very commonly used to communicate with customers. This is true for just about all industries, but is certainly the case with banks, other financial organizations, insurance, etc. Loss of FAX machines (or servers) can really disrupt communications with customers.
FAX machines are pretty easy to find - they may be published on websites and can also be found by war dialing (simply calling numbers and looking for FAX machines/tones). Once the attacker has access to the number used by one or more FAX machines, it is very easy to execute a DoS attack. The attacker does not have to generate actual FAX calls - they simply need to call the FAX number. The FAX machine will normally try to connect (typical time is around 45 seconds) before it gives up. An attacker can easily overwhelm a single FAX machine by simply manually calling over and over. The attack can obviously be even more effective if they are automatically generating calls. If the attacker has access to SIP and can generate multiple/many calls at one time, they can overwhelm multiple FAX machines or a FAX server with multiple concurrent call capacity.
There isn't a lot of simple countermeasures to these attacks. You can change numbers, perhaps timeouts on FAX machines, monitor CDR for wardialing, etc. Of course you can also deploy Voice/VoIP firewalls on FAX machine trunking.