Paul's ministry spanned thirty-five years, from his conversion in 33 A.D. to his death in 68. Surprisingly, the Bible records only three times the apostle was officially arrested. He may have been taken into custody other times, but Luke (who wrote Acts) and Paul saw fit not to record them.
Apostle Paul's first arrest took place in 49 A.D. during his second missionary journey. He encounters, in Philippi, a demon possessed female slave who generates a sizeable income for her owners (Acts 16:16). He ultimately casts the disobedient spirit out of the slave, but only after she carries out a prolonged period of bothering him (verses 17 - 18).
The angry owners of the slave, knowing they can no longer profit from her demonic services, arrest both Paul and Silas. The two evangelists, after appearing before Philippian magistrates, are beaten and placed in prison (Acts 16:19 - 23). They spend less than a day in jail, however, as a miraculous earthquake frees them and all the prisoners (Acts 16:19 - 40).
Chaos in Jerusalem
The second time Paul was arrested, which was prophesied to occur (Acts 21:11), had a monumental impact on his ministry. It took place immediately after completing his third missionary journey.
The Apostle, who wished to show his fellow Jews he was obedient to God's laws (in spite of rumors to the contrary, Acts 21:20 - 21), visits Jerusalem's temple. Jews from Asia, however, recognize him and accuse him of polluting God's house of prayer (verse 28). Their cries for help stir up the huge crowd and cause a riot!
Paul is quickly taken into custody by the Romans to determine whether he broke the law (Acts 22:24 - 30). This action will set off a chain of events that will cause him to be detained by Rome from 58 to 63 A.D. This arrest is also noteworthy as it leads to several recorded firsts.
1) The first and only recorded time the apostle's use of his Roman citizenship saved him from a severe beating, a scourging that could have taken his life (Acts 22:24 - 29).
2) The Roman military (Acts 21:31 - 40, 22:24 - 29, 23:10, etc.) is dragged into the conflict between Paul and the Jews.
3) The apostle experiences his initial interaction with the Roman judicial system regarding his teachings (Acts 23:33 - 24:22).
4) Paul's invoking of his Roman citizenship status leads to his first face-to-face meeting with Caesar (Acts 25:11 - 12, 21).
5) The apostle experiences his first personal confrontation with the Sanhedrin, the highest Jewish religious authority (Acts 22:30 - 23:9, 25:1 - 2, etc.). He also, for the first time, is confronted by the High Priest as a Jewish heretic (Acts 23:2 - 5).
The journey to martyrdom
Paul is arrested, sometime during his final missionary journey, for the third and last time. He is taken against his will, in either late 67 or early 68 A.D., back to Rome. Instead of being held in a secure home, as was the case during his first custody in the Empire's capital, he is now housed in a jail cell.
The apostle writes his last epistle, a heartfelt letter to Timothy (2Timothy), while he awaits his verdict. He is kept a prisoner until around May or June of 68 when he is martyred (which he expected, see 2Timothy 2:9, 4:6 - 8) by the Roman Empire.
Conclusion
The Bible records the Apostle Paul is arrested three times. These lead to a total of roughly five and one-half years spent in custody either waiting for a trial or held until he is martyred.