Jesus tells us that we, as his followers, will not only be able to work all the wonders he did, but more.
John 14:12-14 12 “I assure you: The one who believes in Me will also do the works that I do. And he will do even greater works than these, because I am going to the Father. 13 Whatever you ask in My name, I will do it so that the Father may be glorified in the Son. 14 If you ask Me anything in My name, I will do it.

There are numerous examples of this happening in the book of Acts.

The apostles are suddenly able to speak in foreign languages, able to tell people about Jesus in their own tongue.
Acts 2:1-11 When the day of Pentecost had arrived, they were all together in one place. 2 Suddenly a sound like that of a violent rushing wind came from heaven, and it filled the whole house where they were staying. 3 And tongues, like flames of fire that were divided, appeared to them and rested on each one of them. 4 Then they were all filled with the Holy Spirit and began to speak in different languages, as the Spirit gave them ability for speech. 5 There were Jews living in Jerusalem, devout men from every nation under heaven. 6 When this sound occurred, a crowd came together and was confused because each one heard them speaking in his own language. 7 And they were astounded and amazed, saying,“Look, aren’t all these who are speaking Galileans? 8 How is it that each of us can hear in our own native language? 9 Parthians, Medes, Elamites; those who live in Mesopotamia, in Judea and Cappadocia, Pontus and Asia, 10 Phrygia and Pamphylia, Egypt and the parts of Libya near Cyrene; visitors from Rome, both Jews and proselytes, 11 Cretans and Arabs—we hear them speaking the magnificent acts of God in our own languages.”

The apostles performed many signs, including healing those who were tormented by evil spirits.
Acts 5:12-16 12 Many signs and wonders were being done among the people through the hands of the apostles. By common consent they would all meet in Solomon’s Colonnade. 13 None of the rest dared to join them, but the people praised them highly. 14 Believers were added to the Lord in increasing numbers—crowds of both men and women. 15 As a result, they would carry the sick out into the streets and lay them on cots and mats so that when Peter came by, at least his shadow might fall on some of them. 16 In addition, a large group came together from the towns surrounding Jerusalem, bringing sick people and those who were tormented by unclean spirits, and they were all healed.

Peter healed a man who was lame.
Acts 3:1-7 Now Peter and John were going up together to the temple complex at the hour of prayer at three in the afternoon. 2 And a man who was lame from birth was carried there and placed every day at the temple gate called Beautiful, so he could beg from those entering the temple complex. 3 When he saw Peter and John about to enter the temple complex, he asked for help. 4 Peter, along with John, looked at him intently and said, “Look at us.” 5 So he turned to them, expecting to get something from them. 6 But Peter said, “I don’t have silver or gold, but what I have, I give you: In the name of Jesus Christ the Nazarene, get up and walk!” 7 Then, taking him by the right hand he raised him up, and at once his feet and ankles became strong.

The apostle Philip cast out evil spirits.
Acts 8:5-7 5 Philip went down to a city in Samaria and proclaimed the Messiah to them. 6 The crowds paid attention with one mind to what Philip said, as they heard and saw the signs he was performing. 7 For unclean spirits, crying out with a loud voice, came out of many who were possessed, and many who were paralyzed and lame were healed.

Philip is teleported by the Holy Spirit after baptizing someone.
Acts 8:36-40 36 As they were traveling down the road, they came to some water. The eunuch said, “Look, there’s water! What would keep me from being baptized?” [37 And Philip said, “If you believe with all your heart you may.” And he replied, “I believe that Jesus Christ is the Son of God.”]38 Then he ordered the chariot to stop, and both Philip and the eunuch went down into the water, and he baptized him. 39 When they came up out of the water, the Spirit of the Lord carried Philip away, and the eunuch did not see him any longer. But he went on his way rejoicing.40 Philip appeared in Azotus, and he was traveling and evangelizing all the towns until he came to Caesarea.

Peter heals a man who was paralyzed.
Acts 9:32-35 32 As Peter was traveling from place to place, he also came down to the saints who lived in Lydda. 33 There he found a man named Aeneas, who was paralyzed and had been bedridden for eight years. 34 Peter said to him, “Aeneas, Jesus Christ heals you. Get up and make your bed,” and immediately he got up. 35 So all who lived in Lydda and Sharon saw him and turned to the Lord.

Peter raised a woman from the dead.
Acts 9:36-41 36 In Joppa there was a disciple named Tabitha, which is translated Dorcas. She was always doing good works and acts of charity. 37 In those days she became sick and died. After washing her, they placed her in a room upstairs. 38 Since Lydda was near Joppa, the disciples heard that Peter was there and sent two men to him who begged him, “Don’t delay in coming with us.” 39 So Peter got up and went with them. When he arrived, they led him to the room upstairs. And all the widows approached him, weeping and showing him the robes and clothes that Dorcas had made while she was with them. 40 Then Peter sent them all out of the room. He knelt down, prayed, and turning toward the body said, “Tabitha, get up!” She opened her eyes, saw Peter, and sat up. 41 He gave her his hand and helped her stand up. Then he called the saints and widows and presented her alive.

Slightly less laudatory, but still interesting are the stories about Saul, who became Paul and wrote the majority of the New Testament (that isn’t the Gospels)

Paul caused a sorcerer to become blind.
Acts 13:9-11 9 Then Saul—also called Paul—filled with the Holy Spirit, stared straight at the sorcerer 10 and said, “You son of the Devil, full of all deceit and all fraud, enemy of all righteousness! Won’t you ever stop perverting the straight paths of the Lord? 11 Now, look! The Lord’s hand is against you. You are going to be blind, and will not see the sun for a time.” Suddenly a mist and darkness fell on him, and he went around seeking someone to lead him by the hand.

Paul gets bitten by a poisonous snake and isn’t harmed.
Acts 28:1-6 Once ashore, we then learned that the island was called Malta. 2 The local people showed us extraordinary kindness, for they lit a fire and took us all in, since it was raining and cold. 3 As Paul gathered a bundle of brushwood and put it on the fire, a viper came out because of the heat and fastened itself to his hand. 4 When the local people saw the creature hanging from his hand, they said to one another, “This man is probably a murderer, and though he has escaped the sea, Justice does not allow him to live!” 5 However, he shook the creature off into the fire and suffered no harm. 6 They expected that he would swell up or suddenly drop dead. But after they waited a long time and saw nothing unusual happen to him, they changed their minds and said he was a god.

So now, knowing this – go heal people in the name of Jesus!

(All verses are from the Holman Christian Standard Bible)