In the most popular evangelical scenario, Paul wrote his Pastoral Epistles last--1 and 2 Timothy and Titus. At least since F. F. Bruce,  it is very popular to think that Paul appeared before Nero at the end of Acts and then was released. Paul then would have spent a couple additional years travelling around the Mediterranean, a time when he wrote these three letters, before being arrested again and finally martyred by Nero.
This is an ingenious reconstruction, even if it is only about fifty years old. It stitches together scattered comments in Paul's writings and makes them into a "fourth" missionary journey beyond the so called three missionary journeys of Acts. In Romans 15 Paul says he plans to go to Spain. So perhaps after release from Rome, he conducts a missionary journey in Spain. In Philemon he tells this slave owner to prepare a guest room for him. Perhaps he wrote this letter from Rome and later visited Colossae. In Philippians he says he expects to visit them. Perhaps he wrote this letter from Rome and later visited there.
This reconstruction can also accommodate scattered comments in the pastoral letters themselves. For example, when did Paul leave Titus behind at Crete? There is no really obvious place in Acts where Paul would have been to Crete. Indeed, Acts does not even mention Titus anywhere. And when exactly did Paul leave Timothy behind in Ephesus? Paul did leave Ephesus in Acts 20:1, but did he leave Timothy behind in a pastoral role? After all, Timothy seems to be with Paul in Macedonia just thereafter (e.g., 2 Cor. 1:1).
2 Timothy clearly seems to picture Paul in his final round with Caesar in Rome. So when did Paul leave Trophimus sick at Miletus, on the cost of Asia Minor (2 Tim. 4:20)? When did he leave his cloak and parchments in Troas (2 Tim. 4:13)? A fourth missionary journey provides a convenient way to account for all these intentions and details.
But this scenario also faces serious, if not fatal difficulties. For various reasons, it seems quite likely that Paul was actually put to death at the end of Acts after appearing before Nero. This is in fact the traditional understanding we find up until the late twentieth century. Certainly we cannot just assume such a tradition is correct, but it is also the strong implication of Acts itself.
The argument for Paul's death at the end of Acts is two-fold. First, the latter chapters of Acts consistently foreshadow Paul's impending death. Secondly, Acts was very likely written after Paul's death. The author of Acts thus knew the outcome of Paul's trial before Nero, and he foreshadows it having a negative result. These dynamics seem fatal to this popular reconstruction, coupled with other problems with details. See the endnotes for further details. 
 E.g., Paul: Apostle of the Heart Set Free ***
 You'll have to buy the book when it comes out ;-)