I wish to take a much closer look at the theology of the death of Jesus. I understand that the evangelical position is largely that he had to die to pay for our sins but I fully expect that there are other views within traditions I am much less familiar with but also what objections might be raised to these views.
What is an overview of how the different traditions answer "did Jesus have to die?"
What you are basically asking is for different models of soteriology, which is a fancy way of asking: "What must I do to be saved?"
Typically there are three general schools of thought, grouped into:
Only Satisfaction Theory requires Jesus to die. Ransom theories see it as part of the plan and may or may not require it. Moral Influence theories see the fact that Jesus was killed as a scandal that ought not have occurred.
The simplest theories to understand are the Moral Influence theories. Typically associated with the Eastern Orthodox and yet often ascribed to Augustine and Peter Abelard, these theories focus on Jesus' teachings as the primary mode of salvation. It essentially says if you can learn from Jesus' example, you can be a good person. (Yes, the evangelical in me is saying: "But what about total depravity? - we'll get there.) In a form, this is also the position of many liberal Protestants today in practice - from the emergent church to Deists of all stripes.
Ransom theories & the Christus Victor model focus on the fact that Jesus, in dying, somehow conquered Satan. The powers of evil, having had taken possession of the Earth in the Fall, held sway until Jesus defeated Satan in Hell. As Gutav Aulen writes of this: "the work of Christ is first and foremost a victory over the powers which hold mankind in bondage: sin, death, and the devil." It too is ascribed to the earliest Church Fathers, and held sway until Anselm, Archbishop of Canterbury, introduced substitutionary atonement in the 11th Century. Anabaptists, Peace Churches, and people like Marcus Borg tend to focus on this view. Rob Bell also espouses this view in "Love Wins," but Christianity Today explains its perceived shortcomings as essentially ignoring the fact that Scripture rarely tends to separate the satisfaction piece from the victory piece.
Finally, you have correctly identified the substitutionary atonement models as the primary models used by Evangelicals. Substitutionary Atonement models of salvation essentially view Christ's sacrifice as in terms of either satisfying God's wrath (aka Satisfaction theory) or paying some legal penalty (aka Penal theory of atonement). Adherents tend to be older Protestants and was definitely the mindset of Lutherans, Calvinists, and the other reformers. Indeed Penal theory is essentially a sine quo non of Reformed theology.
