Are there any core beliefs that all Christian traditions agree on? Are there any that most (>90% of) Christian traditions agree on?
If a list can be made for either, are there any caveats?
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Like Narnian commented, per the definition given by this site, nothing. However, historically most denominations have agreed upon several things.
The first thing that comes to mind is the existence of both God and Jesus. Also, many agree Jesus is God.
Again, I say historically - these documents have existed for practically two thousand years with general assent by 97% of Christians (the Chalcedonians).
But again, I stress, precious few doctrine are agreed upon by everyone. There's always someone who may call himself a Christian who disagrees with anything you say. For example, some people call themselves (I say that will all due respect, I'm not saying their not) Christians because they like Jesus's teaching, but don't even believe in a God.
Since "Christian" comes from "Christ" (Jesus), I think the only thing you can safely assume is that all "Christians" have some level of respect for Jesus.
The only way this question can be answered is to agree on a definition of Christianity itself that people have to agree to in order to be a part of that set. People who don't subscribe aren't Christian and therefore their deviance doesn't count. With all of the different religions claiming to be Christian, obviously that does not exist. There are even folks around here who would claim Christianity shouldn't even be deist. Never mind doctrines about Christ, they would said God doesn't exist.
That being said, there are many creeds and confessions that have helped to define boundaries for Christian churches throughout the ages. You are probably familiar with many of them such as the Apostles Creed, the Nicene Creed, etc. One of the major purposes of these statements is to draw lines between what basics must be agreed upon in order to be considered "Christian". The contents of these creeds is probably what you want to hear for an answer. These are the basic tenets of the faith we claim to have in common (if we agree on a given creed).