Both researching ancestors and researching the descendants of ancestors have a long tradition among family historians. I grew up with several books detailing the descendants of prominent ancestors, usually the first in my family line to join The Church of Jesus Christ of Latter-day Saints. However, it is predominant among beginning researchers to focus on establishing an ancestral line rather than jumping back in time to begin research on a remote ancestor.
Fortunately, recent developments in software for family research have emphasized examining descendancy lines rather than focusing on extending ancestral pedigrees. Two of the prominent programs in this regard are the recently introduced Descendancy View in FamilySearch.org and the independent program called Puzzilla.org. Both of these programs prove valuable in establishing a beginning point for descendancy research. But it is important to realize that there are fundamental and inherent differences between investigating backwards in time as opposed to finding the descendants of any person in coming forward in time.
In all cases, when starting with a remote ancestor with the objective of identifying his or her descendants, it is imperative that we are reasonably sure that we have a verifiable relationship with the remote ancestor. Merely picking a name and assuming a relationship is not sufficient. Many members of the Church are confronted with extensive pedigrees in the FamilySearch.org Family Tree program which are completely unsupported by sources. In these cases, careful examination of the ancestral lines is necessary even when the remote ancestor is commonly accepted as a progenitor.
When working backward along family lines we are used to investigating documents in a progression showing parentage. Reversing the process and discovering children involves a more expansive examination of documents with which most family historians may have little or no familiarity. One factor in doing this type of research is the fact that you will inevitably encounter people who are living if you are successful in your research. You may find that the living people object to their inclusion in your genealogy and even object to your whole project of creating a descending pedigree.
Many Church members today are becoming involved in descendancy research with the objective of finding additional family members eligible for Temple ordinances. It is important to realize that the same considerations concerning careful research and verification of sources applies to investigating a family's descendants, as applying to ascendancy research. I have been hearing recently a number of comments concerning individuals who have used the descendancy features of both FamilySearch.org and Puzzilla.org to arbitrarily choose an ancestor and merely click on descendancy links until a possible candidate is identified. No thought is given to the actual relationships and certainly no thought is given to whether or not the information is well-founded.
Before attempting to find the descendants of any particular individual it is very important to establish a clear ancestral relationship with the individual selected. It is also equally as important to identify and document the descendants before making the assumption that there is a "cousin" relationship.