Luke and Acts constitute a substantial portion of the entire New Testament (approx. 25%), so it is no surprise that there are a number of unique elements of this portion of Scripture. The following are various elements of Luke and Acts that are unique to the New Testament or in their specific purpose and goal.

Luke has a lot of material that is unique only to his Gospel...

The Gospel of Luke was written using various sources and information (Luke 1:3), and we see this in the similarities of content that Luke shares with the Gospel of Mark. However, there is a lot of material in Luke that is not found in any other of the Gospels. The following is the material that is unique to this Gospel.

(1) The Infancy Narratives (Chapters 1-2)
(2) Luke's Distinctive Genealogy (3:23-28)
(3) Five Miracle Stories
         Miraculous Catch of Fish (5:1-11)
         Raising the son of the widow of Nain (7:11-17)
         Healing of the crippled woman (13:10-17)
         Healing of the man with dropsy (14:1-6)
         Healing of the ten lepers (17:11-19)
(4) Other Vignettes
         Mary and Martha (10:38-42)
         Zaccheus (19:1-10)
(5) Fourteen distinctive parables
         The two debtors (7:40-43)
         The good Samaritan (10:29-37)
         The insistent friend at midnight (11:5-8)
         The rich fool (12:13-21)
         The barren fig tree (13:6-9)
         Building a tower (14:28-30)
         Preparing for war (14:31-32)
         The lost coin (15:8-10)
         The father and the two sons (15:11-32)
         The prudent steward (16:1-9)
         The rich man and Lazarus (16:19-31)
         The servant's duties (17:7-10)
         The unjust judge (18:1-8)
         The Pharisee and the tax collector (18:9-14)
(6) Certain episodes in the passion narrative, like the trial before Herod and the words from the cross (23:6-12, 34, 40-43, 46)
(7) The resurrection appearances, especiall the Emmaus experience (24:13-53)

(Taken from An Introduction to the New Testament: Contexts, Methods, and Ministry Formation by David A. deSilva, pg. 315.)

Luke is unique in its place in the New Testament because it has an intentional second volume, the book of Acts...

Luke and Acts make a special contribution to the New Testament because not only do they contain material not found anywhere else in the New Testament but because they are written to "tell the story" that we could not piece together without Luke's writings.

Acts contains a number of unique elements in the New Testament...

Acts contains a number of unique and significant elements that are found nowhere else in the New Testament. The following are just a few of those elements.

-- The preaching of the Apostles and others in the life of the early church
-- The history of the spread of the church from vastly Jewish to primarily Gentile
-- The story of the conversion and ministry of Paul (formerly known as Saul of Tarsus)
-- Insights into the missionary nature of the early church

For these reasons and other it is important to read, study, and appreciate the contribution of Luke-Acts not only to the New Testament but to our understanding of God (a.k.a. theology) and our understanding of the nature and mission of the church.