What are the guidelines for call signs for aircraft dealing with US ATC?
According to JO 7210.3Y, Air Traffic Organisation Policy, section 4-4-2 there are several requirements from both the FAA and FCC. The FAA requirements are (paraphrased from the JO):


Comply with FCC regulations (remember that the FCC is responsible for radio communication technical regulations, not the FAA)
Get FAA approval "to avoid possible duplication or conflict
with air−ground call signs assigned on a national
basis to other aircraft operators"


The FCC requirements are in 47 CFR 87.107 (not 87.115 as the JO says):


  (a) Aircraft station. Identify by one of the following means:
  
  (1) Aircraft radio station call sign.
  
  (2) The type of aircraft followed by the characters of the
  registration marking (“N” number) of the aircraft, omitting the prefix
  letter “N.” When communication is initiated by a ground station, an
  aircraft station may use the type of aircraft followed by the last
  three characters of the registration marking. Notwithstanding any
  other provision of this section, an aircraft being moved by
  maintenance personnel from one location in an airport to another
  location in that airport may be identified by a station identification
  consisting of the name of the company owning or operating the
  aircraft, followed by the word “Maintenance” and additional
  alphanumeric characters of the licensee's choosing.
  
  (3) The FAA assigned radiotelephony designator of the aircraft
  operating organization followed by the flight identification number.
  
  (4) An aircraft identification approved by the FAA for use by aircraft
  stations participating in an organized flying activity of short
  duration.


In other words, your call sign must be approved in advance by the FAA, otherwise you can't legally use it per FCC regulations. In reality, if you call up ATC as Little Piggy 27 you'll either get a laugh and a "no, seriously?" or - in the worst case - you'll just annoy them.

There are also military call signs in use but I know nothing about them. I do remember being in the pattern while an Air National Guard aircraft out of Memphis, TN was doing touch and goes using the call sign Elvis 1. But I have no idea how that call sign was set up between the ANG and FAA.