When quoting the number of citations for each paper you have published, different sources can be used, Google Scholar, ResearcherID, Scopus. Google Scholar covers a larger range of literature.
Is it acceptable to use Google Scholar? Or it is not a professional resource, and we necessarily should use ISI Web of Knowledge for counting citations?
None of the citation databases are particularly good. Google Scholar tends to err on the side of inclusiveness (thereby over-representing impact), while the more curated databases (e.g., ISI WoK) tend to err on the side of exclusiveness (thereby under-representing impact). This is particularly acute in some fields: computer science, for example, is notoriously under-represented in the curated databases to the degree that it has is own independent citation database, DBLP, which of course has its own different problems.
You can potentially use any of these databases reasonably to report citations in a reasonable and professional manner, as long as you are consistent and make it clear which database you are using, such that readers can adjust their expectations accordingly.
Google Scholar is actually quite useful, insofar as it draws a broad net for publications, whereas many other citation databases fail to capture important papers. Unfortunately, Google Scholar also has some problems with double-counting, since it often treats different versions of the same articles as if they were different publications, which can artificially inflate citation count. A secondary problem with Google Scholar (which also applies to other citation databases) is that it gives "raw" citation counts (and derived metrics like H-index, etc.) rather than "author adjusted" metrics. This also artificially inflates citation count, especially for authors who do most of their work with a substantial number of co-authors.
One problem with Google Scholar is that its broad sources for papers means that it can be subject to manipulation by publishing mock papers that give no scholarly contribution but give citations to other works or to each other (see e.g., López-Cózar et al 2012). The more tightly curated citation databases do not have this problem since they only count publications in approved sources; typically these sources are established scholarly journals with effective peer review processes.
As the other answer here points out, none of the citation databases are very good. They all suffer from under- or over-coverage and most do not make a serious attempt to adjust metrics for authorship. Personally, I think Google Scholar is less bad than many of the others, since it at least captures all the important papers a person has written, rather than artificially excluding those that fall outside a narrow range of journals. However, you should be aware of its drawbacks in relation to other citation databases and ensure that you carefully inspect the individual publications when using it as an evaluative source.
