At present, different administrations, from universities till WikipediA, become to request a list of citations of a scientist. Moreover, they often require of him to follow one or another certain database.
Certainly, a citation list is an important characteristic of a scientist, unless he is a genius. A genius needs no citation list. I keep my citation list because, time by time, somebody says me that my works are very abstract and mathematically sophisticated, and nobody reads them.
There are different citation databases. A problem lies in the following: (i) none of them is complete, (ii) they do not separate self and non-self citations, (iii) they treat a work published in different issues (e.g., in a journal and arXiv) as different publications and, thus, double a number of citations in this work. To obtain a real picture of citations, one therefore should use several databases.
Let me restrict my consideration to publications in theoretical and mathematical physics.
The ISI Web of Knowledge database (http://www.isiwebofknowledge.com/) certainly is most recognized. However, it is not free, but only by subscription. Therefore, I use it only on an occasion. It does not separate self and non-self citations. The main disadvantage of this database is that it takes into account only references in journals of ISI Journal List, but not in other issues, e.g., books, papers in arXiv and others.
The citation search in AMS database (http://www.ams.org/mathscinet/) covers a wider cycle of issues in mathematical physics, but it is rather young, and is by subscription. I use it on an occasion, too.
In comparison with ISI Web of Knowledge, Google Scholar (http://code.google.com/p/citations-gadget/) takes into account any issue, including the electronic ones. However, it possesses all three above-mentioned disadvantages. I complement it by search in Google Books (http://books.google.com/books) and, directly, in Google.
Some years ago, I followed the Hep Search (High-Energy Physics Literature Database) (http://www.slac.stanford.edu/spires/hep/search/), but it mainly is concerned with references to papers in arXiv. At present, these references can be found in “Experimental full text search” of arXiv itself (http://xxx.lanl.gov/find/), however this search fails to be complete.
I also would recommend SAO/NASA Astrophysics Data System (ADS Harvard) (http://adsabs.harvard.edu/) and SCIRUS (http://www.scirus.com/srsapp/).
For search of citations in journals of IOP Science (http://iopscience.iop.org/journals), Springer ( http://www.springerlink.com/ ) and AIP (http://scitation.aip.org/search_scitation), one can use their own databases, which are rather complete.
As my experience shows, by use of all these database, I however can collect only about 80% citations of my works.