As Edwin Ashworth points out, the four items form two pairs, based on internal contrast within each. It's somewhat elliptical, perhaps even poetic, in that it leaves out an "and" between the two pairs. Also it would sound awkward to say "I share many of the same hopes and fears, and dreams and disappointments." The more standard form "...hopes, fears, dreams(,) and disappointments" would lose or obscure the contrasting pairs. Instead, this construction is analogous to "I share the same hopes, fears." In this case, each pair could be viewed as a unit: "I share many of the same X and Y" where X stands for hopes-and-fears, etc. So, the ellipsis is the omission of "and" BETWEEN the pairs. I think only euphony or poetic intent justifies the construction.