I recently made my citations profile on Google Scholar public. Even though I am not going to have the sort of prolific research program like those of my colleagues at R-1 institutions, I still find it helpful to track the impact of the articles I have either authored or coauthored. It is helpful to have data on the impact of one's articles for any of a number of reasons, ranging from curiosity to making a case for promotion or tenure. Some promotion committees will take into consideration not only the number of peer review publications a faculty member has generated, but also how often each article is cited. Article impact is not currently considered at my present institution, although as the institution becomes more "publish or perish" I can imagine issues regarding impact will emerge as faculty come up for promotion in the near future.
Beyond the need to make a case for promotion, I find it helpful to track new citations to my previously published work (something I refer to my methods students as "treeing forward") in order to conveniently discover other relevant research pertaining to my areas of expertise. Certainly, I want to keep up with any possible replications and extensions of my previous work, as well as to find out what new research avenues have been opened by my work and the work of my coauthors. Obviously, as a scientific writer, I publish to be read. Hence, I am now using the My Citations profile as a diagnostic tool, in hopes of determining appropriate potential journals for future submissions, and to rule out journals that appear to be inadequately cataloged.
Although I usually consider the Social Science Citation Index as the definitive source for tracking new citations, the Google Scholar search engine is pretty impressive, and useful when working at a smaller university without SSCI access.