Personally, I like the h-index best because it is well established and relatively simple to understand. However, it needs to be expressed along with the date and the data source used. Any of these measures ought to be presented along with some explanation and/or examples of well known researchers' scores, to give it context. Sometimes, researchers are asked for their h-index, but if their g-index or m-index score is more impressive, then why not give that too?
h-index – an author with an index of h has published h papers each of which has been cited in other papers at least h times: there’s a great Wikipedia article about it. http://en.wikipedia.org/wiki/H-index
g-index – while the top h papers can have many more citations than the h-index would suggest, the g-index is the highest number g of papers that together received g squared or more citations. This means that the g-index score will be higher than that of the h-index. (I found this explanation at: http://www.researchtrends.com/issue1-september-2007/from-h-to-g/ )
m-index (aka m-quotient) - h/n, where n is the number of years since the first published paper of the scientist. (supposedly handy to differentiate between authors of different vintage in the same discipline)
contemporary h-index –where younger papers accrue higher weightings for each citation, as calculated (and documented) on Publish or Perish (http://www.harzing.com/pophelp/metrics.htm#hcindex).
hI-index – This takes account of co-authorship also documented on Publish or Perish.
hI, norm index – see Publish or Perish
hm-index – see Publish or Perish
AWCR - see Publish or Perish
AWCRpA - see Publish or Perish
AW-index - see Publish or Perish
i10-index – Gscholar “My Citations” gives me this score: “i10-index is the number of publications with at least 10 citations. The second column has the "recent" version of this metric which is the number of publications that have received at least 10 new citations in the last 5 years.”
n-index - Researcher's h-index divided by the highest h-index of the journals of his/her major field of study (n is the first letter of Namazi) Proposed in an article at: http://dx.doi.org/10.4103/0378-6323.62960
A-index – average no. of citations in the article set that makes up the Hirsch core. (Hirsch core is the set of articles whose citation scores count towards the h-index score.) The muddled explanation is mine but you can read about it properly at: http://eprints.rclis.org/bitstream/10760/13282/1/hIndexReviewAlonsoCabrerizoHerrera-Viedma.pdf An excellent article reviewing these measures, published in 2009.
R-index - square root of the sum of citations in the Hirsch core (in the same article linked above!)
m-index – (yes, it looks like another type of m-index entirely & probably explains why the measure listed above is also known as the m-quotient) the median number of citations received by papers in the Hirsch core. See the article linked from my A-index explanation.
NB there are many other measures explained in that article, but by this point I gave up trying to understand them! I quote from the conclusion of that paper instead:
that many h-index variations, although being designed to overcome some of its supposed limitations, do indeed correlate quite heavily. This fact has made some researchers think that there is probably no need to introduce more h-index variations if it is not possible to prove that they are not redundant in real examples.”The article also concludes: “h-index is quite dependant on the database that it is used and that, in general, it is much more difficult to compute those indices using Google Scholar than ISI Web of Science or Scopus.”
GScholar Metrics use different metrics again which sound like the h-index, but these are really aimed at publication level rather than the author… see: http://scholar.google.com/intl/en/scholar/metrics.html#metrics And indeed Scimago will give you an h-index for a publication, and others have calculated h-indexes and variations of h-indexes for departments and groups of authors.
So, which index has your vote?