What was theatre like between the fall of Rome and the Renaissance? Was it open to everyone? What were some famous plays of the time period?
Theatre in the Middle Ages is a difficult construct to identify. For years, historians claimed that very little theatrical activity occurred in years after the dissolution of Roman power networks due to a mistrust of theatre from the Roman Catholic Church and a general loss of literacy and leisure activity. There has been a lot of recent scholarship that is pushing back against these claims. I will summarize quickly and offer some readings that may be of help. First, Greek and Roman dramatic texts survived the growing Germanic transitions of power and were largely used in monastic schools to teach spoken Latin, rhetorical tropes, and classical models of writing/dialogue. Courtney M. Booker in his book Past Convictions, argues that dramatic models were employed in the documenting of events and individuals during the Carolingian Period. Second, the Middle Ages also sees the rise of Liturgical Drama. Most historians point to the 10th century development of the 'Quem quaeritis' trope sung during the liturgy as a mimetic device. For more on that and the early development of Liturgical Drama see Glynne Wickham's The Medieval Theater and for a newer approach see Donnalee Dox's The Idea of Theater in Latin Christian Thought. In these two examples, it was mostly clergy and aristocratic networks that had access to dramatic material and possibly participated in it. There are few distinct plays that develop from this earlier period except those by Hrotsvitha of Gandersheim (based upon classical Roman models); but even that is problematic because there is little evidence that these plays were widely circulated. It's not until the 12th century that we see a larger development of original dramatic material. I'm going to point to the Jeu d'Adam (Play of Adam) as an example of extra-liturgical drama written and performed in the vernacular, likely for lay and clerical audiences. For more about medieval theatre in this period see Carol Symes' A Common Stage. After the institution of the Corpus Christi festival in the 13th century many parts of Europe begin writing plays that were performed by local groups or communities to celebrate this festival. That is what eventually gives rise to the English cycle plays that were performed each year in various English towns by local guilds. These plays were extremely popular and although they featured Biblical themes and stories, they were performed by locals in the vernacular for the townspeople. The York and Chester cycles are still performed often in England today. Any work by Alexandra F. Johnston will be especially illuminating about that particular subject.
Sorry for the length but the Middle Ages is a very long period covering a massive geographic area. I tried to offer some key points and if you'd like more clarification, please let me know. And just in case you're curious: I'm currently a medieval theatre PhD student focusing on dramatic activity in the Early and Central Middle Ages.