What is the appropriate vertical datum to use globally?
In a recent study, Talone et al. (2014) compare 4 different geoids and evaluate their effects for oceanographic studies. The four geoids they used are:


  
  EGM96: The Earth Geopotential Model 1996 embodies ground-based as well as satellite measurements (Lemoine et al. 1998). Remotely sensed data were mainly radar altimeter observations, averaged and transformed in gravity anomalies as expressed in Sandwell and Smith (1997). This geoid may be downloaded from the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center web page (http://cddis.gsfc.nasa.gov/926/egm96/egm96.html). In this study a 360-degree and -order version of the EGM96, included in the GOCE User Toolbox (GUT), was used. GUT is distributed by the ESA at http://earth.esa.int/gut/. In the spatial domain, the geoid is defined on a 0.5° uniform grid. Since the calculation of the EGM96 geoid included altimetry measurements, we may expect that it might have been influenced by some signal from the MSS fields.
  GRACE05: The Gravity Recovery and Climate Experiment (GRACE) (Tapley et al. 2004) is a joint mission by the American (NASA) and the German (DLR) space agencies, launched in March 2002 with the objective of making detailed measurements of the Earth’s gravity field. GRACE’s data are available on the web pages of these two institutions (http://podaac.jpl.nasa.gov/grace and http://isdc.gfz-potsdam.de/grace). As for EGM96, the GRACE05 geoid used in this study is included in the GUT (see Foerste et al. [2008]). It is characterized by a spatial resolution of 0.5° and a spherical harmonic degree and order 360. GRACE05, in the version used for this study, includes altimetry measurements.
  EGM2008: The Earth Gravitational Model 2008 is described in Pavlis et al. (2008) and distributed by the International Centre for Global Gravity Field Models (http://icgem.gfz-potsdam.de/ICGEM/shms/egm2008.gfc). It is available up to spherical harmonic degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159. For consistency with the EGM96 and GRACE05, the geoid heights have been calculated using up to the spherical harmonic degree and order 360, with a spatial resolution of 0.5°. Like EGM96, EGM2008 is the outcome of fusing different data from several sources, including altimetry data.
  GOCE’s level 2 time-wise product: The time-wise product is obtained using only direct measurements of the gravity field, without any altimetry contribution. Details about the GOCE mission can be found on the ESA web page (http://earth.esa.int/GOCE) and in the ESA (1999) report; data may be accessed on the ESA web page. Three different products are available, namely the direct solution, the space-wise solution and the time-wise solution; the last of these was used in this study as it does not rely on auxiliary information (EGG-C 2012). We used the third release, the last one available at the time of the study, based on 16 months of data collected over 18 months (from November 2009 to April 2011). The spatial resolution of the GOCE level 2 products is 0.5°, with degree and order 250.
  


Talone, M., Meloni, M., Pelegri, J. L., Rosell-Fieschi, M., &amp; Flobergaghen, R. (2014). Evolution of geoids in recent years and its impact on oceanography. Scientia Marina, 78(2), 155-164.