In John 14:12 Jesus said, "I tell you the truth, anyone who has faith in me will do what I have been doing. He will do even greater things than these, because I am going to the Father." Does this mean you and I can do even more amazing miracles than Jesus performed while He was on earth. No way!
In this verse Jesus is saying that His many followers would do things greater in extent (all over the world) and greater in effect (multitudes being touched by the power of God). During His short lifetime on earth, Jesus was confined in His influence to a comparatively small region of Palestine. Following His departure, His followers were able to work in widely scattered places and influence much larger numbers of men.
Jesus in this verse was thus referring to "greater works" in terms of the whole scope of the impact of God's people and the church on the entire world throughout all history. In other words, Jesus was speaking quantitatively, not qualitatively. The works are quantitatively greater because Christ's work is multiplied through all His followers.
The Book of Acts provides plenty of evidence that the beginnings of Christ's prediction were fulfilled in the activities of the early church. Indeed, Christianity spread like wildfire, and many wonderful miracles were performed in His name.
It is interesting to note the view of some scholars that even these works done by Christ's followers all over the world are not done independent of Christ. After all, it was He who sent the Holy Spirit to human beings following His resurrection and ascension into heaven (John 15:26), and it is the Holy Spirit who enables believers to do these mighty works (see Acts 1:8; Romans 15:19; 1 Corinthians 12:7-11). Jesus is also certainly involved in answering the prayers of His followers (see John 14:13-14; 16:23-26).