The argument has been made, starting with C.S. Lewis but followed by others, that Jesus of Nazareth was either a liar, a lunatic, or he was Lord. Here's how the argument works:
Liar: Either Jesus was a liar, making false claims to deity in order to gain some kind of power (which is unlikely because he did nothing in his life to take power for himself)
Lunatic: Or Jesus was a lunatic insofar as he really believed he was who he said he was and yet actually died for this identity, even though it wasn't true.
Lord: Or he was and is Lord, he was actually who he said he was.
But nowadays, anyone who leaves the argument there is not really addressing the questions of scholarship let alone the questions of culture. The presupposition behind the "Liar, Lunatic, or Lord" argument is that Jesus actually was going around making claims to deity. However, In actuality, Jesus said a lot more about the Kingdom of God than he ever said about himself. It is arguable whether or not Jesus saw himself as God and it the nature of such knowledge is debatable as well. It is true that, if we are to trust the gospel accounts, Jesus saw his vocation as wrapped in with that of Yahweh. He did see his work as strangely bound-up in what God was doing in the world. And Jesus also saw his life as caught-up with God's presence with and in his people.
People will often look to the Johannine gospel account rather than the synoptics to argue that Jesus thought he was God: they'll look at Jesus saying, "I am the way, the truth, and the life. No one comes to the Father except through me..." as the ultimate claim to deity. But John 14:6, taken literally with context--also considering that Rabbis sometimes referred to the Torah as the Way the Truth and the Life--would be a claim to being the Torah itself or incarnate. Now some may have seen Torah as an incarnation of God, but few would have argued that the Torah is God. Jesus' way may be the exclusive hope for salvation, but that does not necessitate a claim to divinity... in fact, it's far-fetched to say so since Jesus' references to "the Father" imply a separation of identity. The same is true of verses such as "I and the Father are one." A claim to oneness with God is close, but is not the same as a claim to divinity. The simple phrase "I and the Father...," once again, implies a separation with which monotheistic trinitarian theology must deal but it does not necessitate that Jesus thought of his oneness with God the same way we usually do. Whereas John's gospel does little to necessitate a rational understanding in Jesus' mind of his own identity as divine, the synoptic gospels do even less.
All this is not to say that Jesus was not God, in fact I truly believe that He is, but it is to say that Jesus may not have thought of himself that way, and he certainly didn't go around making broad claims to deity. Therefore one could accept that Jesus did not have to be crazy to think of himself the way he did--as uniquely involved in God's work in the world and in the coming of God's Kingdom (in fact, many saw themselves this way and were essentially wrong). He may very well have been wrong in his claims but his willingness to die for them may still be rational, that is, if ever a willingness to die for something can be rational. Martyrs die for similar beliefs and we don't need to say that they're lunatics. If he was a liar then he was bad at it, for his lies profited him only death. Therefore Jesus could have been a liar, a lunatic, the Lord, or he may have been none of the above if the presupposition that Jesus thought he was God is wrong. He may just be misunderstood by interpreters who assume his claims were irrational is not true. Thus the "liar, lunatic, or lord" argument gets us nowhere among savvy scholars. If we're going to continue to affirm Jesus' divinity then we need to find the right starting point for our rational, and I would say that this is totally possible.
As I said before, I would argue that Jesus is God, that he saw his vocation as such and that his presence and solidarity with people was God's presence and solidarity with people. I would make the claim that Jesus' death on the cross was God's death on the cross. I would base this partly but not solely on Jesus' claims about his work and identity. The primary basis of this claim is what we have after the fact. What do we do with all that Jesus said and did? What does it say about God and God's Kingdom? After the culminating event of Jesus' life, i.e., the resurrection, we have the responsibility of working out theologically what has happened. There is no other conclusion which makes sense of what Jesus said and did, in embodying God's Kingdom and bringing salvation, other than the conclusion of his shared identity with Yahweh. This is how the first Christians eventually dealt with it and it's the only way for us to do so. The place to start then is not the claims of Jesus but the response of the disciples after Jesus' death. We can make sense of Jesus' claims only after we've seen them embodied in his death and resurrection. Many would-be Messiahs came and went, preached and were crucified. Disciples would would go back to their trade after their Messiah failed, as the disciples of Jesus did after his death (remember that Jesus came to some of his disciples after his resurrection while they were fishing in John 21). But what could have prompted the disciples to continue Jesus' ministry other than resurrection. Perhaps either they were liars, lunatics, or the resurrection had indeed brought the reign of God through Christ into the world.