Do not neglect the gift you have, which was given you by prophecy when the council of elders laid their hands on you. (1 Tim. 4:14)
Do not be hasty in the laying on of hands, .... (1 Tim. 5:22a)
Therefore let us leave the elementary doctrine of Christ and go on to maturity, not laying again a foundation of repentance from dead works and of faith toward God, and of instruction about washings, the laying on of hands, the resurrection of the dead, and eternal judgment. (Heb. 6:1-2)
What is ordination? In the life of a (especially traditional) church, ordination is normally seen as a formal ceremony in which a person is ordained into an office of a church (normally elders and ministers - teaching elders), accompanied with the laying on of hands. Texts such as 1 Timothy 4:14 and 2 Timothy 1:6 are appealed to, which are said to show Timothy as having been ordained into his office of an elder in the church of Ephesus. (1 Tim. 1:3), which church tradition confirms (Eusebius, Church History, 3.4.6; in NPNF2-01).
According to the traditional reading of these texts from Timothy, Timothy shows us the example of ordination with the laying on of hands, and therefore all elders and teaching elders (ministers) are to be ordained to their office(s) with the laying on of hands. This formal ordination is the formal recognition of God's call to ministry. As Protestants, we do not accept the Roman sacrament of holy office, which is to say we do not hold that ordination imparts a material grace upon its recipients. Since grace is relational and judicial (legal), not ontological, therefore ordination is the recognition of God's call. Most certainly, at the occasion of an ordination, God could grant spiritual gifts (charisma) like in the case of Timothy (1 Tim. 4:14), but the granting of spiritual gifts must be seen as a separate occurrence to that of ordination, which is the recognition and installation into an office.
Now, since it is nowhere explicitly stated in Scripture that Timothy, or Titus too for that matter, are elders, as opposed to mere apostolic workers, it is not surprising that this traditional interpretation of these texts have been questioned by biblicists. That Timothy was an elder is not explicit in Scripture and, since Eusebius' Church History is not Scripture, and not very reliable according to modern history standards, doubt has been cast on Eusebius' portrayal of Timothy as being the bishop (episkopos; ἐπίσκοπος, translated in the New Testament as "overseer" c.f. 1 Tim. 3:2) of Ephesus. But is such doubt valid?
We note that Scripture teaches only two permanent offices in the New Testament: that of elders or overseers (πρεσβύτερος, ἐπίσκοπος) and deacons (διάκονος). Apostleship by its very nature is extraordinary and for the foundation stage of the Church. While one can claim an "apostolic worker" office, (1) the "apostolic worker" is not mentioned separately in Scriptures so it is not an office, and (2) it is always linked to an apostle so therefore it is transient. Thus, there is no such office and we should not treat it as such
One big indication that the traditional interpretation concerning ordination is correct can be seen in the context of 1 Timothy 5:17-22. We note here that the context is that of elders ruling and teaching the flock, yet in verse 22 we see the command not to be hasty in the laying on of hands, followed by a discussion on sins and good works. This subsequent section on sins and good works can be seen as a discussion following upon the issue of sins and charges of sin against elders as mentioned in verses 19-21, and thus it is meant to show what kind of (major) sins is being discussed that one can charge elders with.
The laying on of hands in this context must be seen as the appointment of elders. Do not be hasty in the laying on of hands, because of the gravity and responsibilities of being an elder. Since Timothy is to appoint elders by the laying on of hands, so he himself by the laying on of hands must be an elder too, as all apostles are as well (c.f. 1 Peter 5:1).
Ordination is the formal recognition by the Church of God's calling. This means that ordination is not absolutely necessary, since God's calling is primary and the formal ceremony of ordination is supposed to recognize God's calling. On the other hand, ordination is not unnecessary, as if one can just claim God's call and ignore how God usually governs His Church. Just as a person can be saved apart from baptism, so likewise a person can be called to the ministry apart from ordination, but that is not how God normally governs His Church. A person called should be ordained by the Church, if he is to take up the office God has called him to.
That has implications for ministry and ordination. If ordination is the Church's recognition of God's call, it stands to reason that all who are called should be ordained. All pastors therefore ought to be ordained if they are to serve in the ministry of the Word, and it is wrong to separate the ministry of Word and the ministry of the sacraments, which after all is just another form of the Word. The idea that a pastor should serve for a few years before becoming ordained has no basis in Scripture, for ordination is not a "promotion" for a minister but it should be his due as the Church recognizes God's call upon the minister's life. A minister that is not to be ordained should logically not be expected to serve as a minister in the church, for the church is telling him both that they do not recognize God's call in his life, and also that they want him to serve as if God is indeed calling him to serve as a minister of the Gospel, which is a total contradiction. If we are to keep ordination as being one of calling, then we cannot turn it into one of rank, as if one group of ministers (e.g. those who have served a certain number of years) has a higher rank than another group of ministers ("new" pastors).
It may be objected that ordination is something serious and requires examination of pastors. Then perhaps all ministers should be examined prior to becoming ministers, for are we to say that an error in administering the sacraments is very serious (thus requiring examinations), whereas we do not have to worry too much about errors in handling the Word of God? Lord forbid we treat the sacraments as of higher value than the Word which gives the sacraments meaning! If a person can be trusted with the greater task of handling the sacred words of God, then he should be trusted with the lesser task of administering the sacraments. To say otherwise is to elevate the sacraments above the Word of God, which is contrary to the teachings of Scripture.
Ordination is important but not absolutely necessary. Against the high church, ordination is not some mystical anointing that elevates the minister to another plane of existence. Against the low church, ordination is necessary as the Church's recognition of God's call. Ministers ought to be properly called and ordained, so that the work of the Church can continue and grow.