A religion started by Sidharta Guatama (Sorry for the misspelling) when recieved enlightement (earning himself the name of buddha, or the enlightened one). The Budha's main enlightenment is that desire is the root of all suffering, and thus desire must be crushed (this state is known as nirvana). Budhism also holds basically that all of physical reality is maya (illusion) that must be transcended.
This is, of course, an overgeneralization. Moreover, different budhisms have different histories of the first Budha and what exactly he taught. It must be remembered that when speaking of budhism, one is necessarily making an overgeneralization as there are many budhisms that differ on many points.
A little more of an in-depth explanation of budhism is essentially this, though: People who are not enlightened are caught within the karmic web of causality. Within this web, when one does karmic actions, they have consequences. To become enligthened is to move outside of the web of karmic actions and for one's actions to no longer operate inside of causality. (as an interesting note, within budhism, there is no such thing as good karma or bad karma, all karma is bad in the sense that it traps one within the web of causality). This web of causality is what is referred to as maya, or the illusion. Once one is enligthened, one is outside of this illusion of causality. One of the causal effects of karmic actions is reincarnation, btw. Thus when one becomes enligthened, one is no longer reincarnated.
Of course, that is merely by choice that one is no longer reincarnated, so there are legends (or beliefs?) about budhas (for budhism generally holds that there are many people, not only sidharta guatama, who have become enligthened) who have chosen to incarnate themselves in order to help those who have not yet reached enligthenment. The specifics are not particularly agreed upon in budhism. Some budhisms hold that there are different levels of enligthenment. In one form of budhism, all of its practicioners take the "bodhisatva vow", which consists of vowing that when the attain enligthenment they will not move entirely out of this world but will stick around helping the unenligthened until every sentient being has attained enligthenment.
Many budhisms believe in a whole pantheon of gods, but these gods are not transcendent in a moral sense, only a physical sense. They are still beings, if extremely powerful ones, who are trapped within the karmic web.
Please note that the above description was of necessity an overgeneralization and that there are probably forms of budhism in which the above does not hold. Some forms of budhism are essentially atheistic in which the point of escaping reincarnation is simply to cease existing, whereas other budhisms hold that there is some sort of existence, better than this one, which one can partake in after achieving enligthenment. Of course, the actual path to enligthenment is generally disagreed upon the most by all of the budhisms, and nearly every way concievable is believed to be the way to enligthenment by someone (though some ways are quite certainly more popular than others).
In discussing the differences between budhism and Christianity, it is difficult to begin because there are so many places to begin. Budhism and Christianity differ in most of their characteristics, though not quite as much as one might think, at first glance.
This, of course, does depend on which version of christianity you are talking about. The religion practiced by Jack Chick, which I like to refer to as Chickianity, has little to nothing in common with budhism (though there is a budhism where you, painting with a very broad brush, attain enligthenment through faith alone), but then again it also has little to nothing in common with rationality, so it's not really a very relevant topic. As I said, I generally limit myself to the christianity which can be accurately summed up in the Nicene Creed and which has generally been held by the Catholic and Orthodox churches (as distinct from the rituals and common practices of those churches).
With this version of christianity, budhism has both a fair amount and very little in common. They of course have much in the way of mechanics in common -- incense, candles, prayers, chants, monks, temples, etc. However, that's not so much saying that the two of them are similar but that neither is particularly inhuman. What they have in common is essentially the belief that ultimate reality is not only not what we currently have, but not like what we currently have.
Now, most people who believe in an afterlife believe that it won't be like the life that we currently have, but a surprising number of belief systems hold that the afterlife is mostly like this one, only better. Now, both Christianity and Budhism hold that the life after this one (if one counts enligthenment and not reincarnation as the afterlife). However, the exact nature of that afterlife has little in common with at least some budhisms. For the ones that basically believe in enligthenment as ceasing to exist, this differs very obviously from christianity because christianity holds that people will continue to exist after death.
Even with budhisms which do believe in existence after enligthenment, Christianity has much more of an emphasis on personal existence. Even in the budhisms which are most similar to christianity, personal existence is not a positive thing, it is a thing to be overcome. Christianity, by contrast, celebrates personal existence and almost revels in it. In the words of G. K. Chesterton, "The oriental deity is like a giant who should have lost his leg or hand and be always seeking to find it; but the Christian power is like some giant who in a strange generosity should cut off his right hand, so that it might of its own accord shake hands with him."
Incidentally, this is somewhat evident in the idea of two lovers being "soul mates". Socrates (who was definitely not a budhist) described love basically as people rent in two by the anger of the gods who are looking for their other half to reunite with. This idea is, while quite a pretty one, definitely not christian. In Christianity, romantic love (eros) is the desire of one distinct person for another distinct person, and why husband and wife are said to become on flesh. They do not in any sense become one spirit. Note: I'm not here making any claims about how marriage is concieved within other belief systems. However, there is something in this distinction which is a bit like the difference in Budhism and Christinaity. Within Budhism, the distinctness of personality ranges from not as important to genuinely bad, whereas Christianity celebrates it.
As for the moralities of Christianity and Budhism, they tend to be pretty similar. Both religions disaprove, in the abstract, of lying, stealing, and killing. Both do it because, more or less, of a belief in the value of all things and that lying, stealing, and killing are acts contrary to that value. (of course, nearly everyone else does too, but that is neither here nor there.)
Both Budhism and Christianity have held a fair importance in missionary work.
Interestingly, both Budhism and Christianity have, loosely speaking, generally placed a greater emphasis on attaining salvation than on understanding it, especially with regards to its mechanisms. Sidharta Guatama had a stock response for questions he thought of little value, "that is not a question which leads to enligthenment". While Jesus would rarely side-step questions that severely, he would generaly eschew dwelling on the mechanics of heaven, "Noone knows the day or the hour...". Of course, this is really only a matter of practicality, but it is often forgotten that religions do have their practical sides.
Actually, many religious people hold that religion is actually the most practical thing in the world. And, when you consider it, there is something to that view. After all, what good does it do you to know what the most painless way to kill a man is when you aren't even sure yet that he should be killed?