Do Evangelical leaders (televangelists, megachurch pastors, etc...) not consider themselves Protestants?

A little bit of apples and oranges here, so if you don't mind me clarifying a few terms here.

Protestantism

In the West, most Christians assume that Protestant means anything "not Roman Catholic." Yes, we're ignoring the Orthodox, but I think a strong working definition of Protestantism would be as follows: Any non-Roman Catholic denomination that split from the "universal church" after the Reformations of the 16th Century (1517 onwards). If you don't like the 'accident of history' definition, there is a belief-basis answer as well - see the other response for that.

Protestants differ in a lot of theology, but share a common belief that the Roman pontiff has no special claim to leadership of the church. In this, Protestants really are just picking up the same argument that the Orthodox had before the Reformation, but there is a theological difference between those that split before 1054 and those that split after 1517. This is both geographical (East vs. West) and in terms of theological emphasis. (No Orthodox mysticism, for example, would ever be confused with, say, Scholastic theology or a Spurgeon outline).

Evangelicalism First off, Evangelicalism is a movement, not a denomination. It is a reformed fundamentalism that tends to define itself as reformed fundamentalism. It stresses literal interpretation of the Bible, a return to holiness, engagement with the culture, tends to be missiological, etc... Interestingly enough, the argument is out there that you don't have to be Protestant to be Evangelical, although many assume you have to be. At the risk of self-promotion, I would suggest a quick look at the history here

Evangelical and Protestant In 2007, Francis Beckwith, slated to become president of the Evangelical Theological Society, became a Roman Catholic. Story here. In the end, the Evangelical society basically pushed him out, asserting that part of Evangelicalism is being non-Papist. Tony Blair, when he "converted" to Roman Catholicism was also considered by many to be an Evangelical, and is still considered by many to be both.

Ecumenicalism Recently, amongst most American Christians, we are living in a post-denominational age. As a practical matter, most Christians tend not to care about governance. In a lot of ways, this was due to the fact that Evangelicalism was a movement rather than a denomination. There was an impulse, regardless of denomination, to return to "the fundamentals." This general reforming trend in church politics, as well as the "Culture Wars" of the 80s in which most Protestants realized they had more in common with Catholics than not, has led to a general diminution of denominationalism in general.

The New Evangelicals So, most mega-church pastors (I'm thinking the Rick Warrens, Lon Solomons, John Piper, etc...) tend to be Protestant and Congregationalist. I suspect the reason is more logistical than anything else - the charismatic leadership of a superstar pastor is harder to sustain in a more hierarchical church. I mean think about it - you're a flashy priest in the Roman Church. You start attracting 4000 people on a Sunday. What are the chances you are going to be left to continue your work without any change in orders from above? Doesn't matter if you're being promoted or told to back off - its just harder to achieve a personal following.

What I think you're seeing is a correlation - mega church stars tend to be Congregationalist, because that's the only way to sustain a personality based ministry, and evangelical because, frankly, evangelical churches are growing really strongly in the United States.

I doubt any of these "stars" are going to be hitting "the evils of papistry" very hard - mostly because I doubt most other Christians care. Are they still Protestant? Sure. Buy 'em a beer and they'll tell you they like the Pope but don't believe he's infalliable. Ask 'em to do deep theology, and they'll tell you why. But is important? No. So, Why do I call them protestant? Becuase of time. Why don't they care? Becuase nobody in their churches does either.