Shepard's is a publisher (now part of LexisNexis) that publishes a series of books called Shepard's Citations. The books contain lists of citations. By looking up a given citation in the Shepard's service you can find citations to all the cases (and selected other materials) that reference the original citation. The process of looking up these citations is known as "Shepardizing."
Shepard's reports are particularly used for determining if a case is still good law. The editors include "signals" that tell you if a case has been overturned, questioned, etc.
Once upon a time, people Shepardized using books. You can still do this if you have the books available, though fewer and fewer libraries stock them. However, Shepardizing online is easier, faster, more accurate and more up-to-date. You Shepardize online through Lexis.com, through Get & Print (if you know the citation) or through BriefCheck (which pulls the citations from Word documents).
KeyCite on Westlaw - Westlaw offers an alternative citator called KeyCite. KeyCite is a usefully souped-up version of Shepard's that groups your results by the extent to which they discuss your case.
For a comparison of Shepard's and KeyCite, see Tobe Liebert's New Shepard's v. KeyCite: How Do We Compare? (1999), William L. Taylor's "Comparing KeyCite and Shepard's for Completeness, Currency and Accuracy," 92(2) Law Library Journal 127 (Spring 2000), Diane Murley's Comparison of Features of Shepard's on LexisNexis and KeyCite on Westlaw (2006), The Case for Curation: The Relevance of Digest and Citator Results in Westlaw and Lexis (2012) and the New Jersey Law Librarians Association's Three citators: a brief test (2011).
BCite on Bloomberg Law - Bloomberg Law released a citator called BCIT in 2008 that was renamed "BCite" in 2011. BCite compared unfavorably to Shepard's and KeyCite in a test discussed in the NJLLA LIB-LOG blog (see Three citators: a brief test).
Makeshift citators - LOIS, Fastcase and Google Scholar each allow you to automatically locate other cases in their database that cite to your case. While these are not comprehensive citators, they do make it easy to find additional cases at no charge.