Randy Susan Myers, author of The Murderer's Daughters, posts the first pages of novels on her site and invited me to participate. I posted what I thought was the beginning of my current novel, Calling Every Good Wish Home. No sooner had I posted it, than bam, I had an idea for a better opening. Which I'm not going to post here because it may change again. (I learned my lesson!) This scene is still in the book, so please do read it; it's just not the first thing we see anymore.
Most writers and editors talk about the importance of the first few lines and pages being intriguing enough to draw the reader in. Of course, this is the primary work of the beginning. But I also find a good beginning does something else: it sets up the ending. To me, there's an added enjoyment of an ending when it's foreshadowed (subtly) by the beginning.
Indeed, that's what Robert McKee says in his book Story, which is one of my writing bibles. He calls the opening the "inciting incident." This isn't necessarily the first page of the story, but is "the first major event of the telling; the primary cause for all that follows." More from Mckee:

Like a few others here, my writing process involves writing the beginning, usually the first 100 or so pages, then writing the end and then filling in the middle. The opening I'm currently working with really informed the ending, which then led me to great stuff for the middle.
I think. I hope. We'll see! If the published version of this novel has a different opening than the one I'm working with now I'll let you know!
Happy writing and reading, and good luck with your own beginnings, middles and endings!