As to the original post by @NickolaosPappa. I have no problem believing that miracles happen today. I think they happen more regularly than the average cessationist might, but far less often than your average charismatic. The vast majority of miracles today, I would argue, fall under the category of spiritual gifts (1 Cor 11-14; Romans 12; Eph 4, etc.).
These include, but are not limited to, the ‘big three’ (languages/tongues, healing, prophecy) and exist for the encouragement of the church and equipping of the church for works of service. My own view of prophecy is a bit more nuanced than DiscipleDave’s as I see this gift going through some major changes as God’s people move into the New Testament. That’s for another time, perhaps.
As to Jesus appearing to Paul. I would suggest that Paul conversion and position among the apostles is seen as unique. Consider:
And last of all he appeared to me also, as to one abnormally born. For I am the least of the apostles and do not even deserve to be called an apostle, because I persecuted the church of God. (1 Cor 15:9-10 NIV2011)
Am I not free? Am I not an apostle? Have I not seen Jesus our Lord? Are you not my work in the Lord? If to others I am not an apostle, at least I am to you; for you are the seal of my apostleship in the Lord. (1 Cor 9:1-2 NIV2011)
For this I was appointed a preacher and an apostle (I am telling the truth, I am not lying) as a teacher of the Gentiles in faith and truth. (1Timothy 2:7)
These seem to me at least to suggest a uniqueness of calling that is not available to the average believe today Namely, that Paul saw Jesus and that Jesus himself chose Paul for this ministry. A point Paul also emphasises in his testimony to King Agrippa in Acts 26:15-18.
Galatians 2:1-10 is also helpful in this point. Namely, that Paul saw his role as apostle to the non-Jewish nations (gentiles) as separate and distinct from the work of the Twelve whose efforts were directed primarily to the Jews.
It is also worth asking what Paul actually saw. Although he says he saw Jesus, Luke in Acts 9:3, 4 & 7 and Paul in Acts 26:15 say that what Paul actually saw was a blinding light. Jesus then spoke to Paul from this light.
So when Paul says ‘I saw Jesus’ I think he is using non-literal language. A bit like when a person says, ‘I saw the President!’. By which they mean, I saw the President’s car drive past.
As to visions/appearance of Jesus happening today. Well, some Muslim (and/or indigenous) converts report seeing a vision of man they later understand to be Jesus, telling them to seek out Christians and the like. I see no reason to doubt such stories. However, I wouldn’t put this in the same category as Paul’s vision on the Road to Damascus, which, both Paul and the New Testament seem to see as a unique commissioning event.