Prior to the year 1234, the church did not have a formal canonization process as such. Also, one must consider the life of the church during the time of Roman persecution, and the life of the church after the legalization of Christianity in the year 313 by Emperor Constantine.
Before the legalization, those holy individuals recognized as saints were martyrs who had suffered during the various Roman persecutions. However, as mentioned in the question, Mary, St. Joseph, St. Elizabeth and St. Zechariah (the parents of St. John the Baptist), St. Ann and St. Joachim (the parents of our Blessed Mother) were also recognized as saints because of their holiness and the role they played in the plan of salvation. All of the apostles (all of whom died as martyrs except St. John who survived the means of execution) were recognized as saints by the early church.
The tombs of martyrs, like St. Peter and St. Paul, were marked and kept as places for homage. Often, altars were built over the tombs of these martyrs, so that when the priest offered Mass in worship of God, the witness of faith of the martyr was remembered and his intercession implored. Also, the anniversaries of their deaths were remembered and placed on the local church calendar. After legalization, basilicas or shrines often were built over these tombs, like St. Peter’s in Rome.
A great example of early church devotion to the saints is that of St. Lucy and St. Agatha, both of whom are mentioned in the Roman Canon (first eucharistic prayer) of the Mass. St. Lucy, who was martyred in Sicily in 304 during the persecution of Emperor Diocletian, had prayed at the tomb of St. Agatha (martyred in Sicily around 200) for relief from the hemorrhages she was suffering. Besides Sts. Lucy and Agatha, all of the saints mentioned in the Roman Canon were highly venerated by the church of Rome in the early fourth century.
After the legalization of Christianity, those who were recognized as “confessors” — who had lived their faith with heroic virtue — were also recognized as saints, for example, St. Hilarion, St. Ephrem, St. Hilary of Poitiers and St. Martin of Tours. Generally, upon the death of a holy confessor, the local bishop conducted an investigation and then declared him “a saint.” As such, these saints could be venerated, their intercession implored, and their tombs honored.
The first recorded canonization by a pope for someone outside the Diocese of Rome occurred in 993: Pope John XV canonized Ulric, bishop of Augsburg, Germany. On the other hand, the last known saint canonized by the local bishop was St. Walter of Pontoise (d. 1095) a Benedictine monk, abbot and reformer who fought against simony and laxity among the clergy; he was canonized by Hugh de Boves, the archbishop of Rouen in 1153.
More and more, appeals to the Holy Father were made for his intervention and approval before a person was canonized, in a sense, “added to the list of official saints.” Moreover, the church saw the need to tighten the canonization process. Unfortunately, sometimes figures of legends were honored as saints. Or once, the local church in Sweden canonized an imbibing monk who was killed in a drunken brawl — hardly evidence of martyrdom.
Therefore, in the year 1234, Pope Gregory IX established procedures to investigate the life of a candidate saint and any attributed miracles. In 1588, Pope Sixtus V entrusted the Congregation of Rites (later named the Congregation for the Causes of the Saints) to oversee the entire process. Beginning with Pope Urban VIII in 1634, various popes have revised and improved the norms and procedures for canonization, even in the last century — Pope Pius XI, Pope Paul VI, and most recently Pope John Paul II in his apostolic constitution “Divinus Perfectionis Magister” (1983) (which interestingly have governed his own canonization process).
In light of the question, remember when our beloved Pope John Paul II died April 2, 2005: People in the crowd of St. Peter’s Square chanted, “Santo subito” i.e., “Sainthood now.” Despite the tremendous popular support for an immediate declaration of sainthood for him, the church still mandated the regular canonization process.
In all, we must not lose sight that this thorough process exists because of how important the saints are as examples for us, the faithful who strive to live in the kingdom of God now and see its fulfillment in heaven. During this Year of Faith, we remember the teaching of the Vatican Council II: “God shows to men, in a vivid way, His presence and His face in the lives of those companions of ours in the human condition who are more perfectly transformed in the image of Christ. He speaks to us in them and offers us a sign of this kingdom to which we are powerfully attracted, so great a cloud of witnesses is there given and such a witness to the truth of the Gospel. It is not merely by the title of example that we cherish the memory of those in heaven; we seek rather that by this devotion to the exercise of fraternal charity the union of the whole church in the Spirit may be strengthened” (“Lumen Gentium,” 50).