Does publishing on Arxiv diminish chances of publishing in a journal/conference? If I publish a paper on Arxiv, does it diminish my chances of getting published at a reputable peer reviewed journal? Does it diminish my chances of presenting my paper at a reputable conference?
In mathematics it is extremely common for people to post their papers to the arXiv before submitting them to a journal. The idea is that this allows them to get feedback on their paper before making the submission. For instance, several of my collaborators have posted all of their papers to the arXiv. Moreover, I have never heard of a journal not accepting a paper due to its having previously been posted to the arXiv. This doesn't mean that there aren't any journals with policies prohibiting arXiv posted submissions, but I cannot imagine any mainstream journal having such a policy as use of the arXiv is so widespread that there would be a big pushback. There are even well-respected arXiv-overlay journals like Discrete Analysis which do not host papers at all but merely link to the relevant arXiv posting.

The bottom line is that when it comes to well-respected math journals, having already posted your paper to the arXiv should have no affect whatsoever on the likelihood of its being accepted to be published by a journal.

Added: One potential exception to what I wrote above are journals with double-blind reviewing systems. Such journals are extremely rare in mathematics, but they do exist (e.g., The American Mathematical Monthly). Posting an article to the arXiv and then submitting it to a journal with a double-blind reviewing system runs the risk of ruining the anonymity of the author.