Well, first let me tell you what I think, then you can take the poll below and/or leave a comment about how you disagree (or agree).
However, before I elaborate my thoughts, here is the summary of my answers to the question.
Yes, sure, I care what the Buddha taught if it is valuable. I know that anti-religion Atheists may not care what any religionist says or said — including the Buddha. But that is potentially their loss. And if you are a Buddhist, you may have much more faith in the Buddha than I do.
How do we know what the Buddha said? That is a tough question. I am not sure about all the textual criticism studies in Buddhism and hope to be pointed to them in the future by readers because of my academic curiosity. But for right now, I suspect much of the Pali canon contains much of his teachings. I suspect that much of the Mahayana canons (Chinese and Tibetan) contain the writings of later teachers (though I am aware of the controversies).
Since we have so much material on the Buddha’s forty years of teachings in the Pali Canon, I think we can agree on the Buddha’s basic teachings and themes. However, many Buddhists radically disagree because they say some teaching supplant others. This happens in Christianity too — with Mormons, Jehovah Witnesses, Seventh Day Adventists and others. But to tell you the truth, it does not really matter to me what the Buddha taught. Instead, I care about the various mental training in all contemplative traditions. I am curious about the methods offered in Buddhist literature (Theravadin and Mahayana) and I don’t mind thinking through and working through the ones I feel are valuable to me whether the Buddha wrote them or not. It just so happens that from my various exposures, I am most sympathetic with the teachings reported to be those of the Buddha.
But if a teaching in Buddhist literature were actually that of a later teacher instead of the Buddha’s, I don’t care. If a later teacher contradicted the Buddha or changed his words, but I think that teacher is right, I will go with the later teacher. So you see — I don’t have any faith in the Buddha (one of the Triple Gems in Buddhism– see my diagram). I feel no need to have faith in any particular person at all. I do understand the comfort of having someone you can imagine your can totally trust, but I lost that feeling a long time ago.
But with all that said, I am impressed by the weight of Buddhist scripture and thus feel that Siddhartha taught some pretty valuable material and in that way I have a measure of trust/faith in the Buddha’s teachings. Much of those writings , art and myths inspire me. However, I think much of Buddhist literature is horseshit, of course — but I am OK with that tension.
As a final note, as far as Christianity is concerned, the only “Yes” reasons I have remaining are the academic reasons plus the ability to work with Christianity’s influence in my society. Oh yeah, and it is part of my past. Any wisdom in the New Testament is shared in many traditions and not unique to Christianity. After all, Jesus came to do (redemption), not teach, right? Anyway, as you can otherwise, the brunt of my evaluations are in the “No” column.