How should data regarding remarriages, adoptions, etc be handled in a family tree? Should extra branches be created for the "spare" cousins, step-relatives, etc? Or is there another way to map the data?
For example, if a grandfather, who was adopted, remarries after his wife dies, how do the "new" additions to the tree need to be represented?
For anyone you want to be included in the tree, you simply need to connect them properly and your genealogy program (hopefully) will handle them correctly.
A remarriage should be handled as a 2nd spouse. If you can give the reason for the end of the first marriage (divorce, separation, death of spouse), include that with the first spouse.
An adoption should be handled by connecting the adoptee to the adoptive parents in a parent-child relationship. You should mark that connection as an adoptive relationship, which most programs will allow you to do. Foster relationships should be done the same way. Biological parents (if different than the legal parents - e.g. proven through DNA) should be done this way as well (if you want to record this - may be a privacy issue).
If this is done and your program is "smart", it should be able to figure out the step-family, half-family, adoptive family, legal family and biological family relationships correctly.
If your program is not "smart", then be assured that this is still the correct way to enter the data, even though your program cannot display it correctly. Don't be swayed into doing it any other way or your relationships will get messed up when you transfer them to another program or an online tree.
This is really up to the historian. If you would like to track this information then you should keep it in your tree. If not you can remove it. It should be noted that just because a person is divorced it does not mean there is no blood relationship for that branch of the tree.
If you decide to keep the information many of the software packages have support built in. For example with Mac Family Tree, there are event types for marriage and divorce. I child could be biological or adopted. A child can belong to two family units, adopted to the father, biological to the mother in on family and the opposite in the other.
Although practicality will depend on the software you're using, my belief is that only biological lineage can be used to directly link people in your data, i.e. links from children-to-parents.
This, in turn, is based on the fact there there is a set number (2, even if not yet known), that their relationship is fixed and not time-dependent, and the relationship can be unambiguously defined.
All other relationships, including step-parents, guardians, adoptive parents, foster parents, or even masters in the context of slave families, can be represented through the use of a role vocabulary. We already see this in census pages, and take for granted roles like: Head, Wife, Step-son, Wet-nurse, or Visitor.
What I'm suggesting is that all these non-biological relationships (including the many forms of marriage) can be represented in the data using roles in relation to some common event (e.g. census, birth, baptism, marriage, etc).
Of course, how your software presents this to you could be a challenge but this answer relates to the data itself, as indicated by the question.
{edited} To put biological lineage on a par with social connections, including adoption/foster relationships, is not right. As said above, the biological links are fixed, whereas a "step family" or "foster family" may only exist over a given interval. One of my own parents was fostered, but broke all ties with that family when they were adopted, and then broke all ties with that family when they married.
