Most recently, I auditioned and got cast in a local college's production of Richard III, and (being the type of anal-retentive, detail-oriented* person I am) have spent an inordinate amount of time researching background details of the time period, history & lineage of every character in the play. SO, since I already spent the time researching, I figured it might be beneficial to others if I posted my resulting compiled information.
This is a simple family tree diagram showing what the "House of York" and "House of Lancaster" mean. Edward III had 5 sons, and the houses are the descendants of those sons. As you can see in the diagram, the descendants of Lionel & Edmund eventually intermarried, causing theYorkist reunion line, otherwise known as the House of York. Descendants of John of Gaunt are of the House of Lancaster. Edward's line died out, and Thomas's line simply remain considered part of the House of Pantagenet (which York & Lancaster are offshoots from).
The following chart may be hard to read unless you view the full version, but it shows the relationships of (most) of the characters in the play. To add to the confusion, the play references some characters by their given name, and some by their title, so I have listed both where applicable.
During my research, I also found that many of the spouses of play characters had the last name Neville, so I did research into that and added a smaller family tree for the House of Neville (which are also descendants of John of Gaunt... see above diagram) to explain the relationship between them.
Other notes about the above diagram: Margaret of Anjou / Mad Margaret is also known as Queen Margaret, and similarly Elizabeth Woodville / Lady Grey is also known as Queen Elizabeth, and her daughter Elizabeth of York is also called Princess Elizabeth.
The characters I haven't listed on the above charts are due to my difficulty in finding their connection to the throne. Every person with a title should be of the peerage (nobility, related to the royal bloodline), but information on little known persons is hard to come by. The one relationship that I was able to ascertain is that the Duke of Norfolk (John Howard) is the father of the Earl of Surrey (Thomas Howard).
Here is a list of the historical personages I have been able to connect with the characters of the play. Surname P stands for Plantagenet, character names listed within parentheses are dead, and links are to the relevant Wikipedia page.
There were also several characters we cut out of the play, who are not included above.
I would also like to thank Corinna Archer's Richard III Casebook blog as it was very helpful for research & inspiration for me posting my findings.
richardiiicasebook.blogspot.com
*Yes, I realize that's redundant, however, since most people aren't familiar with the term "anal retentive," I felt it was necessary. Congratulations for being intelligent enough to catch it.