How many stereogenic centres are there in discodermolide?
Summary

The confusion probably arises because of incompletely standardized definitions of at least some subset of the words "stereocenter", "stereogenic", "stereogenic center", "stereogenic unit".

IUPAC definitions

The place to turn for authoritative definitions of these terms is IUPAC's Gold Book, as noted by @jerepierre in the comments.  Here is what it has to say:


  stereogenic unit (stereogen/stereoelement)
  
  A grouping within a molecular entity that may be considered a focus of stereoisomerism.
  
  At least one of these must be present in every enantiomer (though the
  presence of stereogenic units does not conversely require the
  corresponding chemical species to be chiral). Three basic types are
  recognized for molecular entities involving atoms having not more than
  four substituents:
  
  
  A grouping of atoms consisting of a central atom and distinguishable
  ligands, such that the interchange of any two of the substituents
  leads to a stereoisomer. An asymmetric atom (chirality centre) is
  the traditional example of this stereogenic unit.
  A chain of four non-coplanar atoms (or rigid groups) in a stable conformation, such that an imaginary or real (restricted) rotation
  (with a change of sign of the torsion angle) about the central bond
  leads to a stereoisomer.
  A grouping of atoms consisting of a double bond with substituents which give rise to cis-trans isomerism.
  


Thus, the unequally substituted C=C moieties in discodermolide are "stereogenic units" according to IUPAC.

Stereocenter

Unfortunately, this term is not defined in IUPAC's Gold Book.

Stereogenic center

Unfortunately, this term is not defined in IUPAC's Gold Book.

Wikipedia

Wikipedia is not as authoritative as IUPAC but it is likely that chem.se readers will encounter wikipedia entries for these terms far more often than IUPAC's in the course of regular web searching.

Stereogenic unit

No Wikipedia entry

Stereogenic center

Redirects to "stereocenter", see below.

Stereocenter


  A stereocenter or stereogenic center is an *atom* bearing groups such that an interchanging of any two groups leads to a stereoisomer.


This definition does not apply to C=C double bonds, because only an atom can be a stereocenter, not a group of atoms.  Supporting this interpretation is a complete lack of reference to cis-trans isomerism on the rest of the page.

Usage by chemists

Discodermolide is referred to in many sources as having 13 "stereocenters" or "stereogenic" centers.  This conforms with the Wikipedia, atom-centric definition of stereocenter.  Here are some example sources:


Wikipedia's discodermolide article: (+)-discodermolide has
...13 stereogenic centers... 
A presentation from 2004:
molecule possesses: 13 stereocenters 
A paper from 2003: Paper title: Regulated-Stereoselective Construction of Thirteen
Stereogenic Centers...


All these uses comport with both Wikipedia definitions of "stereocenter"/"stereogenic center".  Chemists do not seem to use the IUPAC term "stereogenic unit" very much in actual practice.   I could not find any relevant pages using both the term "discodermolide" and the phrase "stereogenic unit", for example.  

Bottom line

It is just possible to pass a thread of consistency through the eye of this needle of confusing terminology.


Discodermolide has thirteen (13) stereogenic centers.
Each of those stereogenic centers is by definition also a stereocenter, and is also a "stereogenic unit".
In addition to those 13 stereocenters, there are three additional "stereogenic units" in discodermolide corresponding to the unequally substituted C=C bonds.