The prevailing view (not unchallenged) among both critical and pious scholars is that Luke was the last of the synoptic gospels to be written. In other words he wrote after Mark and Matthew but prior to John. This is based on the so-called Markan priority view of the synoptic problem according to which both Luke and Matthew used an existing version of Mark plus the sayings source "Q" and their own particular other material. Presuming that this is correct, when Luke spoke of "many others," he referred to Mark and possibly Matthew, as well any unknown other accounts and legends he may have been aware of, but which have since been lost.
Whether he referred to Matthew, however, is debatable, because they wrote at roughly the same time. He may or may not have known of Matthew's Gospel. Other accounts he may have known of include:
The Gospel of Thomas. Several scholars think Thomas was written prior to Luke, although this is by no means the consensus view.
Sayings Source Q. Both Matthew Luke included many saying from this hypothetical source in their work. It apparently once stood on its own, and Luke may have thought of it among his "orderly accounts."
Nativity and infancy stories. Several such narratives were probably circulating, onceone of which (centering on Joseph rather than Mary) was included by Matthew but not Luke. In this category we may also include infancy and boyhood narratives such as the one Luke tells of Jesus in Lk. 2, about the presentation in the temple and the boy Jesus teaching the elders. Some of these stories seem to have found their way into later works such as the Infancy Gospel of James and the Infancy Gospel of Thomas.
Resurrection accounts. Even the canonical gospels give varying details about this important issue, and later apocryphal gospels go further. Luke may have referred to a wide variety of such legends, thinking that his work would provide clarity to his readership.
Other Acts. Finally, since Luke and Acts are generally considered as being written by the same author, the prologue to Luke could refer to apocryphal or lost "acts" as well as gospels. In other words, "the events that have been fulfilled among us" could mean of works done by the various apostles, including collected miracle stories and martyrdom accounts.
Conclusion: By "many" Luke could have meant what we would call "several." He probably referred to Mark and possibly Matthew. But since even "several" is more than two, it is probable that he was also thinking of other early gospels, birth narratives, infancy stories, resurrection accounts, apostolic acts, and collections of sayings of which he was aware but which are now lost.