I've heard people criticize the Bible for not taking a harder line against slavery. The general defense that Christians make (and it's a good one) is that slavery was a fact of life in Biblical times; the Bible isn't a political treatise intended to reform temporal governments, but rather a spiritual treatise intended to bring all men and women into a relationship with God through Jesus Christ. Critics say that passages that mention slavery appear neutral towards the institution at best:
1 Corinthians 7:17-24
Nevertheless, each one should retain the place in life that the Lord assigned to him and to which God has called him. This is the rule I lay down in all the churches. Was a man already circumcised when he was called? He should not become uncircumcised. Was a man uncircumcised when he was called? He should not be circumcised. Circumcision is nothing and uncircumcision is nothing. Keeping God's commands is what counts. Each one should remain in the situation which he was in when God called him. Were you a slave when you were called? Don't let it trouble you—although if you can gain your freedom, do so. For he who was a slave when he was called by the Lord is the Lord's freedman; similarly, he who was a free man when he was called is Christ's slave. You were bought at a price; do not become slaves of men. Brothers, each man, as responsible to God, should remain in the situation God called him to.
As the passage makes clear, the point is that we should keep God's commands rather than worry so much about our earthly situation. Nevertheless, if a slave can gain freedom -- or a totalitarian dictatorship can gain democracy -- he should do it.
However, last week while preparing for my small group at church I did find one passage that explicitly condemns slavery:
1 Timothy 1:8-11
We know that the law is good if one uses it properly. We also know that law is made not for the righteous but for lawbreakers and rebels, the ungodly and sinful, the unholy and irreligious; for those who kill their fathers or mothers, for murderers, for adulterers and perverts, for slave traders and liars and perjurers—and for whatever else is contrary to the sound doctrine that conforms to the glorious gospel of the blessed God, which he entrusted to me.
So here's a list of evil acts (a common thing to find in Paul's writings) with a member that isn't found elsewhere: slave trading, which presumably inclues slave owning.