Some of these gifts were a part of the same system, sharing a specific task. Since all divine power was not given to anyone person (except Jesus), they were all needed in sharing their gift.  1 Corinthians 12:27-30 reads,
Now you are Christ’s body, and individually members of it.  And God has appointed in the church, first apostles, second prophets, third teachers, then miracles, then gifts of healings, helps, administrations, various kinds of tongues. All are not apostles, are they? All are not prophets, are they? All are not teachers, are they? All are not workers of miracles, are they? All do not have gifts of healings, do they? All do not speak with tongues, do they? All do not interpret, do they? Â
Here, Paul combines the evangelists, pastors, and teachers of Ephesians 4 into one category; namely, teachers.  These gifted men were gifts given to the ekklesia (Ephesians 4: ).  However, the list continues to mention gifts of the Spirit that are comparable to the gifts mentioned in 1 Corinthians 14.  They were spiritual gifts of miracles, healings, helps, administrations, and tongues/interpretation.  They could covet certain gifts but the ultimate choice appears to be the Spirits.
Another similar passage that lists gifts of the Spirit is in Romans 12:3-8.  They appear to be broader categories of service that may include different specific gifts in each of the categories listed.  It reads,
For by the grace given to me I say to everyone among you not to think of himself more highly than he ought to think, but to think with sober judgment, each according to the measure of faith that God has assigned.  For as in one body we have many members, and the members do not all have the same function,  so we, though many, are one body in Christ, and individually members one of another. Having gifts that differ according to the grace given to us, let us use them: if prophecy, in proportion to our faith;  if service, in our serving; the one who teaches, in his teaching;  the one who exhorts, in his exhortation; the one who contributes, in generosity; the one who leads, with zeal; the one who does acts of mercy, with cheerfulness. (ESV)
You will note that Paul writes of the one who leads.   1 Corinthians 12:4-11 rounds out the list. It reads,
Now there are varieties of gifts, but the same Spirit;  and there are varieties of service, but the same Lord;  and there are varieties of activities, but it is the same God who empowers them all in everyone.  To each is given the manifestation of the Spirit for the common good.  For to one is given through the Spirit the utterance of wisdom, and to another, the utterance of knowledge according to the same Spirit,  to another faith by the same Spirit, to another gifts of healing by the one Spirit,  to another the working of miracles, to another prophecy, to another the ability to distinguish between spirits, to another various kind of tongues, to another the interpretation of tongues. All these are empowered by one and the same Spirit, who apportions to each one individually as he wills.
No one had all the gifts, but no one is exempt from one, either.  Among those whose sins had been remitted on the day of Pentecost, the promise of His gift was given (Acts 2:38-39). Taking all the passages above and placing them together in one chart, we have that list and description below.   You will see some overlapping and the gifts are distinguished from the gifted men who were given to the people of God, such as apostles, prophets, evangelists, pastors/teachers.  These men probably had more than one gift but what set them apart was their teaching. We know the Apostles had miraculous powers as well as the gift of revelation. Probably, Evangelists and Pastors had more than one, also.