I have been paid to do lots of different types of photography over the years, including weddings. I had always avoided weddings, but eventually, there was a family friend situation that forced my hand, and I did one. Then, from the results of that, I was offered more, and you know how the story goes.
From the first wedding I conducted to the last there were a lot of lessons — some major, some minor. There are certainly borderline objective essentials for wedding photography, but for me, there is something — or rather a group of things — that were essential to me: spare... well, everything.
Of course, you can't have spare everything, but when it comes to batteries, cables, SD cards, and so on, I was always fully stacked and they were all charged, formatted, and ready to go in their individual ways. This is essential to me in more ways than one. Firstly, sooner or later, something will die, fail, or otherwise malfunction and if you don't have a replacement, you are in a bit of a situation. Secondly, even though I've only ever had one real gear disaster (a card malfunctioned and was then unreadable too!), the peace of mind provided by knowing I have an answer to most difficult questions on a wedding shoot is invaluable to me.
What is essential to your wedding photography?