This may be a little provocative - will anybody bite?!
I've been working through the first part of 1 Corinthians, and it hadn't struck me before what a large chunk of the book Paul spends talking about the issue of divisions in the church - basically the first four chapters.
The shape this took in Corinth was people identifying themselves with particular Christian leaders - Paul, Apollos, Cephas (Peter). To try and reduce some of the thoughts in these chapters to a few sentences .... in chapters 1 and 2, Paul says that the message of the gospel (foolishness and weakness in the world's eyes) is undermined by focusing on the wisdom and strengths of Christian leaders. In chapter 3, he shows that the church is one field, one building, and the Christian workers are working for God, not for themselves. In chapter 4, he looks at the impact that following leaders has in the lives of Christians - they become proud and arrogant - again, not where Christians ought to be.
A key line from Paul in chapter 4 is his quote in verse 6 - "Don't go beyond what is written." The basis of our Christianity has to be God's Word - not the words of a Christian leader. Christian leaders only have authority insofar as they are expressing what God has already said.
Christians today are still prepared to line themselves up behind the names of Christian leaders - Luther, Calvin etc. These four chapters really undercut this expression of Christianity. By extension, denominations are effectively the alignment behind different leaders. Paul is quite clear that the basis of Christian co-operation has to be the gospel - in other words, if people don't have that as their foundation, they have already taken themselves "out of the building" - they no longer have the right foundation. But beyond this, if we can accept people as Christian brothers and sisters, what basis do we have for not welcoming them - in biblical terms?
So, rather than organising churches on denominational lines, it would be more appropriate for gospel-declaring churches to co-operate at a local level in whatever way it is possible for the gospel to be made known. Of course we are going to be stuck with the legacy of trust deeds and so on - but as Christians we need to transcend these for the sake of the gospel.