The Intervarsity statement of faith I quoted earlier says that one of its founding principles is the belief in
The unique divine inspiration, entire trustworthiness, and authority of the Bible.
This is a very strong statement about the Bible and its authority, but it is very careful not to say that the Bible is inerrant. I remember that this was an important point during the discussion of whether this statement of faith should be adopted by MIT's Graduate Christian Fellowship. The basic fundamentalist understanding of the Bible is that if it is not a word-for-word dictation from God to the human writers, God at the least vouches for every word. Some evangelicals would agree, but many of them would not go that far. They believe the Bible is what it claims to be, and that God's inspiration made sure of that. Some books of the Bible claim to be direct dictation from God: the prophets, Revelation, and parts of the Pentateuch, for example. On these parts, evangelicals and fundamentalists would be in agreement. The Gospels, however, are a different matter. They claim to be eyewitness accounts (or in the case of Luke, a thoroughly researched history) of the life of Jesus. Thus, when there's disagreement between the gospels, such as the differences between the Resurrection accounts, an evangelical can just say that these differences are no greater than any difference in eyewitness accounts of such an eventful and hectic morning (as Lee Strobel argues in The Case for Christ). The fundamentalist must reconcile these differences, because he believes that any difference would be God contradicting himself.
All fundamentalists hold to sola scriptura, and I’d guess that most evangelicals do, but not all. Sola scriptura is the belief that the Bible alone is the supreme authority for Christian believers, and that all other authority derives from it. On the other hand, the Catholic Church places the highest authority not on the Bible, but on apostolic succession, the idea being that Jesus chose his apostles to be leaders in the Church and gave them authority, who then gave authority to their successors, and so on, through today, where the Pope is the direct heir of that succession. Some other churches also believe in Apostolic succession, such as the Orthodox and Anglican churches, although they don't believe the Pope is the direct heir. As I understand it, the authority granted by apostolic succession weakens the further removed the successor is from Jesus: thus Jesus's own words have absolute authority, the writings of Jesus's apostles have the next greatest authority, then the early church fathers, becoming weaker and weaker throughout the years. Those churches view the Bible’s authority as deriving from apostolic succession, as the Old Testament is vetted by Jesus and the apostles (in Jesus's day, there was disagreement about which parts of the Old Testament were truly authoritative: the Christian church has more or less decided which books had authority according to what Jesus and his apostles said about them, although there are some complications), the New Testament is written by those first apostles, and later codified by others in the early apostolic succession. Therefore, even in the tradition of apostolic succession, the Bible has greater authority than any other writing, but the authority of the apostles is its source.
As I said, evangelicals place great emphasis on the authority of the Bible, although not all of them claim it is inerrant. And while most of them believe that the Bible is the source of all Christian authority, the movement also includes those who believe that the authority of the Bible derives from apostolic succession. All evangelicals believe that the Bible directly applies to their lives, and put great emphasis on studying the Bible and putting it into practice.
Update: Jeremy Pierce of Parablemania has a lot of good comments. Some of them are about details I glossed over in this post, read his comments to find out which. Two of the things he said are pretty important:
I wonder if your explanation on gospel accounts is a dodge. Are there errors in some of the accounts? If so, then even evangelicals are hard pressed to agree. This is perhaps one of the places where some people want to call themselves evangelicals when I'm not sure I want to give them the name. Do they deny the infallibility of the Bible? Perhaps not, but if the gospel accounts are merely reports of what some people remembered, and it turns out that their memory was faulty, it's not an attitude toward scripture that I would consider consistent with evangelicalism.
Jeremy makes a good point, and this is the reason I tend to be more on the inerrancy side of things. Those who claim scripture is authoritative but not inerrant have two points in their favor. The first is that even if the differences in the gospels are errors due to faulty memories, the agreement between them is great enough that no essential Christian doctrines are in question, and are all attested to by multiple witnesses. This isn't a reason to believe it to be the case, but rather a reason that believing it doesn't necessarily put you outside of orthodox Christian thought. The second, and I think more convincing point, is that the gospels don't claim to be divine revelations, or more specifically, the divinity they're revealing is Jesus himself and their accounts of him. Again and again in Acts and the Letters, the apostles use their eyewitness status in their preaching, and the gospels are the eyewitness accounts with some commentary, the amount of which varies from gospel to gospel. I believe that the commentary there is (John has the most) is given the same authority as the Letters, written by those with a special relationship with and knowledge of God, granted authority to be His witnesses.
Evangelicals who believe this don't use their uncertainty to argue against doctrine so much as to reconcile the differences in the accounts. Those who do use this belief to question essential doctrine, such as the Jesus seminar ("Jesus never would have taught his disciples the Lord's prayer!") fall outside my definition of evangelical. Of course, it could be that this belief is more on the left edge of evangelicalism than I realized. Remember, I've lived in Boston for the last seven years.
Jeremy also says he's "never heard of this gradual dilution of authority view before." My "as I understand it" disclaimer probably wasn't strong enough. My knowledge of Catholicism comes mainly from my conversations with Catholics, many self-described evangelicals, rather than personal study of Catholic doctrine. They may have been more atypical of Catholics than I thought, or I may not have understood them very well. I'm fairly certain they held the Bible to be a higher authority than the Church fathers, with less authority being granted to more recent writings. The "dilution" may have been more how I viewed that understanding than they did. They probably would deny there was any conflict between the writings, but I think they would view the Bible as more foundational.