There are many pragmatic reasons why a church might have elders. A plurality of elders can help to carry the burden of pastoral ministry; they can bring a rich variety of experience to bear on the issues and problems every pastor faces; they can hold the pastor accountable in a context of shared ministry; they can save the pastor from a multitude of errors in judgment before it ever becomes apparent in a congregational meeting. The list could go on.
But the best reason a church should have elders is because the New Testament says that it should. Throughout his epistles, and especially the pastoral epistles, Paul makes it plain that every New Testament church should have elders, that is men who "direct the affairs of the church" (1 Timothy 5:17-18). He commissioned Titus to make sure that all the churches in Crete had elders (Titus 1:5). And he took the time to outline for both Timothy and Titus what sort of men should be called to that office (1 Timothy 3:1-7; Titus 1:6-9), as well as the procedure that should be followed should a man need to be removed from the office (1 Timothy 5:19-20). So central were elders in Paul's thinking that, though eager to reach Jerusalem by Pentecost, he took the time to call the Ephesian elders together and give them one last exhortation (Acts 20:16-38), the heart of which was that they be faithful as "shepherds of the church of God".
Of course, elders were not just Paul's idea. Peter too assumed their presence in the churches to which he wrote, and gave them a message identical to Paul's: Be shepherds of God's flock. (1 Peter 5:1-4). So did the author of Hebrews (Hebrews 13:17).
So the Bible clearly teaches that New Testament churches are to be led by elders. At the end of the day, this question is just another way of asking whether or not we are going to allow the Scriptures to be the sole authority in the life of the church. For though there are lots of pragmatic reasons to have elders, from the perspective of a pastor, there are more pragmatic reasons not to have them. Elders can slow a senior pastor down, they can disagree with him, they can even tell him on occasion that he's wrong. Pragmatically speaking, who would want that?
But Peter and Paul remind us that the churches we pastor are not our own. We are pastors of God's church, God's flock. And so it is God's Word that must have the final say. Jesus created the church, he died for the church. He is its only King and law-giver. If we are committed to shepherding Christ's church, and not our own, then we must be willing to do it his way. According to the Bible, his way includes elders.
Further reading: Edmund Clowney, _The Church_ (IVP, 1995) ch. 14; T.E. Peck, _Notes on Ecclesiology_ (repr. GPTS Press, 1994), ch. 16. The problem with both of these recommendations is that they are written by Presbyterians, who claim far more for the authority of elders than Scripture warrants. Nevertheless, they both lay out clearly the argument from Scripture for the presence of elders in the local church.