Among the great families of Christian Churches, there are many which are international in character; however, many of these are not juridical bodies -- that is, they are more like associations, groups of like-minded Churches. When they act, it doesn't affect the local congregations and members. In fact, of all large Christian bodies, there are only four I know who really stand out for their international unity.
The Anglican Communion is one such; however, its unity has been sadly damaged in recent years. At its most basic level, the Anglican Communion is a close association of national Churches, each with its own primate. Some parts want to work closely together, like a single denomination; others want to follow their own way. The inability of the Communion to enforce its rules upon its member units is its weakness.
Eastern Orthodoxy is, in one sense, a prime example of international unity; however, it also has struggles with trying to act together. By its own understanding, it is a union of national Churches, but "national" in the case of the USA tends to mean "ethnic." So, there are multiple representatives of Orthodoxy in America, and their inability to agree on a single primate tends to contradict their own theology of what constitutes an Orthodox Church.
The Roman Catholic Church, in contrast to the AC and EO, is truly united, and there is no doubt who is in charge. All its parts (and they are more varied than most people who are only acquainted with the Latin Rite understand) are accountable to the whole and work together. The parts may squabble with each other from time to time, but the Vatican pulls together truly international gatherings to work on things, and when the Pope speaks, he is obeyed.
Then there is The United Methodist Church. Theologically, we are very like the Anglicans; however, organizationally we are more like the Catholics. All our Conferences, in whatever part of the world they operate, are part of one single connection. Our General Conference speaks for the whole UMC (now, if everybody would just obey it!). In contrast with the RCC, however, we use a democratic process to elect bishops and GC delegates.
I like the fact that we are one, worldwide Church, not just an American denomination with a few outlying missions. I like the idea that our African, Asian, and European UM members and clergy have the same standing our American UMs have. I like the idea that when I go outside the country, I'm still a practicing UM minister among UM Christians, and that our rules and structures are the same.
One thing I would like to change: I'd like to see us bring African UM leaders over here as missionaries to teach us how to evangelize and start churches. Or maybe we need to start sending small teams on American UM leaders over there to learn how it's done. For the teaching ministry flows both ways, and in a truly international Church, anybody can wind up anywhere, doing God's work.
Seen against the backdrop of global United Methodism, the celebrity pastors of America (including Adam Hamilton) seem incredibly culture-bound.