A bow with infinity would be high on my list, so would some feather falling boots. Ender pearls are nice in case your arrival point is not on the main island or if you get knocked off. TNT is good for quickly blasting into the cages around the crystals.
If you want to collect dragons breath, some empty potion bottles are necessary.
To kill the dragon, a good bow is useful, and as Rodabon said FF on boots is a must; the dragon has a tendency to thro you up into the air sometimes. I use ender pearls to reach the caged crystals and just pickaxe a few bits away then jump down and arrow them as per normal (but I suppose TNT would help). Keep out of the breath when it first appears as it can knock your health down quickly; I would take plenty of steak for food as I think its still the best food item, and you will need to top up regularly with all the leaping, running and fighting you'll be doing. I find the dragon tends to fly down over the centre portal and spew his breath for a few seconds every so often; I usually get in behind him in this case (arrows are ineffective when he's in this mode) and can whack his ass with my sword for a good 5-10 secs at a time, so a good sword is recommended too. Sometimes instead of flying away he swivels on the spot and spews more breath; just move accordingly and continue using your sword.
You may also know that you can wear a pumpkin on your head as "armour" which will allow you to look directly at Enderman without them being aggroed. But it limits your vision considerably, I tend to not bother and look down at an angle when I'm running, and when I'm shooting up at the dragon, make sure I'm careful when I'm panning up or down to avoid any enderman in my line of vision. One of the best things to quickly build near the centre out of end stone is a 5x5 square on a 2 high central column (like a mushroom); you can hide under it if gets a bit Enderman crazy, and they cant reach you, but you can chop at the offending Endermen's legs to kill them, and get extra enderpearls as well. In this case, its also useful to have a sword without Fire Aspect on it; Enderman on fire teleport away and can die without dropping pearls or dropping them a distance away from your shelter.
Nobody's mentioned buckets yet? I like using a waterbucket to get up to the caged pillars. Water can help to ward off angry Endermen (if not using a pumpkin) and you can fall into it without taking damage if you get knocked off the pillar.
Biggest reason I didn't mention them is that the Ender Dragon loves flying through them and destroying your water. You'd need to take at least 5 with you.
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Watch out for the crabocalypse. Some say the day will never come. But it will.
Feel free to drop by for a chat whenever.
If you'd like to talk with me about other games, here are a few I play.
Team Fortress 2
Borderlands series (Borderlands 2 is my favorite game, ever. TPS combat is a lot of fun and makes up for the lower-quality story, in my opinion)
Elder Scrolls series
Warframe (IGN is something like That_One_Flesh_Atronach)
Pokémon series (HGSS forever)
Left 4 Dead 2 (Boomer files always corrupt though)
SUPERHOT (SUPERHOT is the most innovative shooter I've played in years!)
Dead Rising series (Dead Rising 2 is one of my favorite games, and the 3rd was a lot of fun. 1st has poor survivor AI and the 4th is bad)
7 Days to Die
Just Cause series
Come to think of it, I mainly play fighting-based games.
In my most recent world I just made it to the end and fought the dragon. I had full Diamond Protection IV, Unbreaking III, Mending armor, half a stack of cooked porkchop (same food value as steak), a couple of golden apples and regen potions, a Diamond Sharpness V sword and a Power V, Infinity bow.
I also had a couple stacks of Cobblestone, some Ender Pearls, two buckets of water and some TNT for dealing with the crystals on top of the obsidian towers, and a stack of glass bottles for collecting Dragon's Breath. I did bring a Pumpkin, but ended up not wearing it. Any Endermen I accidentally agro'd would get killed when I ran under the dragon while it was perched on the exit portal, so it wasn't much of a problem.
And this was all overkill...
In older versions of the game I thought the dragon was way too easy to kill. It was a disappointing boss battle, especially considering it's supposed to be an end game achievement. As long as you had a good bow and were a decent shot you could take out the dragon without even being hit yourself (the dragon would turn away after being shot).
I had really hoped (and expected) the new changes would make the dragon battle more challenging, and some things like the lingering dragon's breath and cages around the crystals do add to the difficulty, but the stupid perching on the portal ruins it. Now you don't even need a good bow (or much bow skill) because you can just stand underneath it and whack away while it is perched on the portal. And once you have destroyed all of the crystals the dragon spends an even longer time perched on the portal, which makes it an easy kill with a good sword or axe.
It amazes me how wrong Mojang gets things sometimes. They tried to make the dragon battle harder, but I think it's actually easier now.
Basically, take a good sword and/or axe, any old bow (and a stack of arrows if you don't have infinity), ender pearls or blocks for getting to the caged crystals (and TNT or a pickaxe to take them out) and decent armor with some food and potions for healing, and you shouldn't have any trouble.
I don't take much at all; basic iron gear with no more than level 1 enchantments, some food, Ender Pearls (in case I spawn off the island), and a bow with at least Power V (several stacks of arrows if it does not have Infinity, which I now only bother with if I happen to get it twice when enchanting my "caving gear", if I do that before going to the End):
(in this case I did put Infinity on my bow, although more recently I have not bothered even if I did get it twice since I've never needed to make more than one bow. Also, you do not need to bring anything with you to get the egg; I use the torches that spawn on the portal)
I did bring highly enchanted diamond armor and that stuff the first time I ever went to the End but like others I found it was overkill; the only time I've ever died in the End was from being knocked into the void, where nothing can save you (unless you manage to throw an Ender Pearl fast enough). I play on Normal but I would simply wear better armor on Hard (1.5x damage = 1.5x protection, which is easy to add). For similar reasons I may consider it in my next world because armor is less effective (diamond is only as good as iron in vanilla 1.6.4, due to less protection per armor point, not because I'm playing in 1.9+) and I'll be breeding villagers so I can get Mending and may as well take advantage of any blacksmiths I get (they sell everything prior to 1.8 so diamond gear is basically worth a few stacks of wheat or other item).