Luke 9:3

In the above verse Jesus gives His disciples no less than six “no” directives – take nothing, no staff, no bag, no bread, no money, and no extra tunic. According to the previous verses, they were only to go in His power and in His authority – that would be sufficient and they were obedient to the command. Later we learn in verse six that they went forth from village to village spreading the good news and healing miraculously:6 So they set out and went from village to village, preaching the gospel and healing people everywhere. Luke 9:6 (NIV)
So why did Jesus want them to go away empty handed according to the worldly way of thinking? While not all circumstances in Scripture are the same regarding this particular issue, I believe in this incidence Jesus had several reasons. One would certainly be that the disciples could not be found trusting in their own resources because they simply had none. This, of course, would result in the strengthening of their faith. Perhaps another reason would be as a benefit for those that they were ministering to. This would provide them an opportunity to offer more than a verbal thank you but rather something tangible that would minister back to the disciples in taking care of their physical needs. Jesus tells us this in Matthew: 10 take no bag for the journey, or extra tunic, or sandals or a staff; for the worker is worth his keep. Matt 10:10 (NIV) The Bible Knowledge Commentary states the following reasons: “People would evidence their belief in the Twelve—and thus in the Messiah—by showing hospitality to these men who were ministering in Jesus’ authority. This helps explain Jesus’ rather strange instructions concerning a method of their ministry. The mission was not to be long—they came back to report to Jesus. Why were the Twelve not to take supplies or money with them? This was because of the brevity of their mission and also because people’s reactions to them would indicate whether or not the nation was accepting Jesus’ claim as the Messiah. People who believed the message and the messianic healings would be glad to share with the Twelve. People who did not believe would be judged. If a town rejected the Twelve the latter were to shake the town’s dust off their feet. When Jews returned home from a Gentile country, they would shake the dust off their feet to signify their breaking ties with the Gentiles. In this way the Twelve signified that certain Jewish townspeople were like Gentiles who would not listen or believe. Jesus was thus giving the entire area opportunity to believe His message and mission.” Interestingly, Paul and Barnabas did this exact display in Acts due to the unbelief of the Jews there: 49 The word of the Lord spread through the whole region. 50 But the Jews incited the God-fearing women of high standing and the leading men of the city. They stirred up persecution against Paul and Barnabas, and expelled them from their region. 51 So they shook the dust from their feet in protest against them and went to Iconium. Acts 13:49-51 (NIV)
Jesus gives us this same principle in Matthew: 11 "Whatever town or village you enter, search for some worthy person there and stay at his house until you leave. 12 As you enter the home, give it your greeting. 13 If the home is deserving, let your peace rest on it; if it is not, let your peace return to you. 14 If anyone will not welcome you or listen to your words, shake the dust off your feet when you leave that home or town. 15 I tell you the truth, it will be more bearable for Sodom and Gomorrah on the day of judgment than for that town. Matt 10:11-15 (NIV)
The idea was that as the apostles ministered, their recipients would in turn minister to them. Showing, of course, a belief in the message they brought. The warning was not very pleasant for the inhospitable! Sodom and Gomorrah ended up “smokin”- not a very pleasant end to say the least! Like the disciples of Jesus’ day, we too have a priceless message to extend to our sphere. Paul tells us:7 But we have this treasure in jars of clay to show that this all-surpassing power is from God and not from us. 2 Cor 4:7 (NIV)
Our message is powerful and comes with authority. Paul also tells us:

17 For Christ did not send me to baptize, but to preach the gospel--not with words of human wisdom, lest the cross of Christ be emptied of its power. 18 For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God.

1 Cor 1:17-18 (NIV)

Lastly, we are told again through the pen of Paul:

14 How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them? 15 And how can they preach unless they are sent? As it is written, "How beautiful are the feet of those who bring good news!" Romans 10:14-15 (NIV)
“Carrying God’s gracious offer involves human beings whom God has brought to Himself and then uses as His heralds. They share God’s message of salvation because He will save everyone who calls on His name.” Bible Knowledge Commentary