There certainly are many people and groups which argue against incorporating churches, but is there a biblical argument for incorporation? Jesus told His disciples in Matthew 22:21, "Give to Caesar what is Caesar's, and to God what is God's." This answer was given specifically to the question of whether it was lawful to pay tribute, or taxes, to Caesar. In Jesus' response, He asked whose image and name was on the money, and, since it was Caesar's, it was therefore proper to give it back to him.
If we apply this principle to the church, it will help us determine the answer to the question of incorporation. The church is a body of believers in Jesus Christ. As a body of believers, we are answerable to God for everything we do. We are also answerable directly to God as individual believers, for we "are bought for a price" (1 Corinthians 6:20). In Matthew 17:27, Jesus taught the disciples that, though they were not compelled to pay taxes, it was proper to do so to avoid offense.
But the state only has secondary authority over the church and the individuals who comprise it, although certainly not over the direction or purpose of ministry, for that is God's realm. Most churches own property, which is administered under the state, and while it may not be absolutely necessary to incorporate in order to hold that property, it is a proper way to do so. Gordon Johnson, in his book My Church (1957) wrote, "In our day most of our states in this country demand trustees for the legal procedure of the church." This is still the case today, and incorporation not only serves as a way to honor the state's realm of authority, but also serves as a legal protection for the individuals in the body. When property is held and actions are taken in the name of a recognized corporate entity, the individual members of that entity are safeguarded from being held personally liable in court actions that may be brought against the incorporated church.
One passage that is sometimes used against incorporation is worthy of mention here. First Corinthians 7:23 says, "You were bought at a price; do not become slaves of men." This verse is irrelevant as an argument against incorporation for a couple of reasons. First of all, it is in the context of human slavery, not church organization. Also, verse 24 states that we are to abide in whatever state God calls us, even if that is slavery. Second, it does give us a warning worth considering in our discussion. Some have argued that when a church incorporates, it places itself under the control of the state (being the servants of men). As the various legal battles over church tax exemption in recent years have shown, there is a possibility of a struggle here, even if it is a remote one. The majority of cases that have come up were because key leaders chose to push the limits of the law (sometimes in order to show that the law was being misinterpreted). Certainly, if the state tries to control the ministries of any individual or church, we are obligated to answer as the apostles did in Acts 5:29, "We must obey God rather than men!"
The underlying question of incorporation is not whether we can or can't incorporate, but in what way we can best serve God and still honor the God-ordained authority of the state. Yes, there are benefits that we can reap from incorporation, but we have to recognize that there are at least potential costs to those benefits. In most cases, we will have no trouble honoring the state's God-given authority while also giving supreme allegiance to God's higher authority.
Note - some advocate that churches seek tax-exempt non-profit status through 508(c)(1)(a) instead of through 501(c)(3). If you are concerned about any of the potential problems mentioned above, 508(c)(1)(a) might be worth looking into.