Of course, death of the author may not seem applicable to what a lot of us write. I would say most people aren't setting out to write a satire of the military-industrial complex. And yeah, excessive analysis of a story can get really, really obnoxious (and is often a fatal flaw of secondary school English courses). This doesn't mean, though, there aren't things which can't be read into a story. Shippers wouldn't exist if there wasn't something, somewhere they saw as giving basis to their preferred couple. Maybe you mean for your hero to have Motivation X, but to Reader A it seems like Motivation L and Reader B sees Motivation Q.
I've been thinking about death of the author recently for three reasons.
1. It's almost 1.30 in the morning and I'm staying up to see if a sick friend is feeling better when they wake up and so I need to find ways to amuse myself lest I start to get sleepy
2. I saw John Green recently state, paraphrasing due to shoddy memory here, "once a book is published it belongs to the readers and not the author". He is like the living embodiment of this concept apparently.
3. I am a bit of a control freak when it comes to my writing. Not that I would be some belligerent god whose word is law, but I am extremely self-conscious with regards to everything, and so for me it is vitally important that a story be 100% flawless before I share it with someone. If it isn't, the moment they find something wrong all hell will break loose. So I feel like my mind might see any interpretations people have which run contra to my intent as a flaw with my writing.
Of course, different authors over the years have had different opinions with regards to the concept. Tolkien himself, while never outright stating it, said things which suggest he was a supporter of the notion. Margaret Atwood, on the other hand, very much wasn't.
Ultimately, I find myself largely apathetic to the concept, at least right now. This may be because I do view myself as writing nothing more than modern pulps, it may be genuine apathy, or it may be because I have no rabid fangirls to present their insane theories to me.
Of course, this is just a simplistic overview. More info may be found on wiki and via googling the term, if you feel you want more.
What about you? Would you embrace the concept, reject it, or just generally not care?