- Man vs. Man: Rather self explanatory, but I will expound. In this category, the conflict resides between two characters or two groups of characters. A few good examples of this are Luke Skywalker against Darth Vader, the little boy from under the cupboard against "He Who Shall Not Be Named", or Huckleberry Finn against...well, everyone, really.
- Man vs. Nature: Jack London's Call of the Wild comes to mind here. A young man striving to survive the wilds of the gold rush era Yukon. Tarzan is much the same, though it is the jungle rather than the frozen tundra. There are elements of the first category in both stories, but it is the wilderness that takes first billing.
- Man vs. Himself: The inner turmoil. To me, the best example of this is Shakespeare's Hamlet. While there is abundant use of Man vs. Man in the play, it is the struggle within Hamlet that drives the character to do the things that he does.
*Cough* Sorry, I digress.
The point is that conflict is necessary. I don't mean that it has to be all out war every time, but there must be a struggle that will ultimately define and propel your characters. It also doesn't have to be so melodramatic as some of the examples I've given. Conflict can also be subtle (Hannibal Lechter's mind games with Clarice), but not so subtle that it is lost to the reader.
Without some form of conflict, nothing would happen. Everything and everyone would be inert (or, at best, ambiguous/apathetic which amounts to much the same thing) and that, from a reader's stand point, is really and truly boring.