The Apostles were the original twelve to fifteen who were directly commissioned by the resurrected Christ. There are no more. Yet their ministry continues through their writings. They continue to build up the church and move her along to maturity. See this post.
Prophets and prophecy are also continuing gifts in the church. See this post first and then this one.
One gift that I have not addressed is tongues. Tongues are known languages. This too, is a continuing gift in the church, as is the interpretation of tongues.
I mentioned in the comment section earlier that I would explain what is wrong with this question: "Why could Paul or Peter heal someone whenever they intended to and we can not?"
This question is based on two assumptions:
1) The Apostles could heal whenever they wanted to, and
2) We cannot heal anyone EVER.
First, the Apostles could not heal whenever they wanted. I am sure that many Christians in the days of the Apostles died of illness. They probably even died when the Apostles were close by. And yet they were not healed.
Second, the gift of apostle and the gift of healing are two separate gifts. Whereas the Apostles are now gone, the gift of healing as a separate gift did not go with them. We do have a prescription for healing, outlined in the letter of James,
Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord. And the prayer of faith will save the one who is sick, and the Lord will raise him up. And if he has committed sins, he will be forgiven. (Jam 5:14-15)This prescription for healing was in effect during the times of the Apostles, and is also available to the church today. If we have not seen the healing of the sick, then we have not practiced God's means for healing the sick.
That's all I have to say about that.-Forrest Gump