Does the human hand have 27 degrees of freedom?
Keeping in mind that I know nothing about this, I will try to explain why the hand can be modelled with 27 degrees of freedom. This is just my interpretation of this paper, which says:


  The human hand has 27 degrees of freedom: 4 in each finger, 3 for extension and flexion and one for abduction and adduction; the thumb is more complicated and has 5 DOF, leaving 6 DOF for the rotation and translation of the wrist. 
  
  To accurately model the hand, a complete model of the muscles, tendons, bones and a neurological control structure is necessary. The dynamics of such a complex model are still poorly understood, forcing the use of simplified models. Current models are too simplified for our purpose so we turn to recent work from the medical community to motivate assumptions used in a new model that we propose here. We use a 27 DOF model of the hand with the following sim- plifying assumptions:
  1. The thumb is independent of the other fingers.
  2. Adduction/abductionofthefingerjointsareindependent.
  3. Motion frequency does not affect joint interdependence.
  4. Both hands have the same interdependence model.
  5. The posture of the wrist and the rest of the arm do not
  affect the underlying interdependence structure.


Incidentally, this implies to me that there are different models of the hand with different assumptions that use a different number of degrees of freedom. 

Anyways, take a look at this hand:


[source]

And now, follow along with your own hand!


finger (4 DOF): each finger has 2 interphalangeal joints between the distal, middle and proximal phalanges that allow for flexion/extension (2 DOF); each finger also has a metacarpophalangeal joint between the proximal phalanx and the metacarpal that allows for flexion/extension as well as abduction/adduction (2 DOF)
thumb (5 DOF): an interphalangeal joint between the distal and proximal phalanges allowing flexion/extension (1 DOF); a metacarpophalangeal joint between the proximal phalanx and metacarpal allowing flexion/extension and abduction/adduction (2 DOF); a carpometacarpal joint between the metacarpal and trapezium allowing flexion/extension and abduction/adduction (2 DOF)
wrist (6 DOF): between the carpals and radius allowing flexion/extension, abduction/adduction and supination/pronation (3 DOF); I think when the authors refer to translation of the wrist, they are simply saying that hand can be moved in all planes of 3D space (ie up/down, side to side, forward/backward - 3 DOF)


Since we have 4 fingers, they give 16 DOF. Adding the 5 DOF of the thumb and 6 of the wrist, we get 27. Please nobody question my reasoning. Thank you.