When replacing non-grounding type receptacles is a GFCI receptacle required, or can any GFCI device be used?
The NEC simply states "where supplied through a ground-fault circuit interrupter" in this instance, so you can achieve this either by a GFI receptacle, a faceless GFI device, or a GFI breaker.

You cannot however use an AFCI breaker, unless it is one of the new (and rare) AFCI/GFCI breakers. Good luck finding one though. I find one Siemens on Amazon and that's about it.

See "(c)" below.

From the 2011 NEC:


  406.4 General Installation Requirements
  
  Receptacle outlets shall be located in branch circuits in accordance
  with Part III of Article 210. General installation requirements shall
  be in accordance with 406.4(A) through (F).
  
  (D) Replacements.
  
  Replacement of receptacles shall comply with 406.4(D)(1) through
  (D)(6), as applicable.
  
  (2) Non–Grounding-Type Receptacles.
  
  Where attachment to an equipment grounding conductor does not exist in
  the receptacle enclosure, the installation shall comply with
  (D)(2)(a), (D)(2)(b), or (D)(2)(c).
  
  (a) A non–grounding-type receptacle(s) shall be permitted to be
  replaced with another non–grounding-type receptacle(s).
  
  (b) A non–grounding-type receptacle(s) shall be permitted to be
  replaced with a ground-fault circuit interrupter-type of
  receptacle(s). These receptacles shall be marked “No Equipment
  Ground.” An equipment grounding conductor shall not be connected from
  the ground-fault circuit-interrupter-type receptacle to any outlet
  supplied from the ground-fault circuit-interrupter receptacle.
  
  (c) A non–grounding-type receptacle(s) shall be permitted to be
  replaced with a grounding-type receptacle(s) where supplied through a
  ground-fault circuit interrupter. Grounding-type receptacles supplied
  through the ground-fault circuit interrupter shall be marked “GFCI
  Protected” and “No Equipment Ground.” An equipment grounding conductor
  shall not be connected between the grounding-type receptacles.