The items are key to any Attack Damage Carry. I will not lie, my build is standard, but has its own little twists. I like to stat out with Boots of Speed with 2x Health Potions and 1 Mana Potion. The Boots will help you to keep moving to collect that farm (or runaway from dying). Since you are a distance fighter, you shouldn't be taking that much damage, therefore you only really need 2x Health Potions to start. The one Mana Potion is a great help, considering Ezreal can use Mana rather quickly, the Mana Potion will help keep you in your lane longer. Next, the two Doran's Blade, although their passive is OK, not the greatest, but their extra health and damage helps give you the upper-hand early game in your lane. Then, the Berserker's Greaves, the extra attack speed works well with Ezreal, and the movement speed buff is a must. Next, Vampiric Sceptar going into Bloodthirster, this is a must to get ASAP, the AD and LS is a MUST for Ezreal. Following after Bloodthirster is Phantom's Dancers, this combo lets you hit hard and quickly and gain health fast when needed. The extra speed buff and critical strike helps out a lot too. Then Furor so you can chase down those enemy champions more quickly. Next, Trinity Force is a must for any Ezreal, the unique traits of Trinity Force fits Ezreal perfectly, and helps give him a bit of a Hybrid Build later game. Then, Black Cleaver, excellent item for those pesty tanks on the enemy team, this will chew them down to size quickly, also the passive of deteriorating their armor for a small period of time helps the rest of your team out to hit the tank hard. Finally, Guardian's Angel is helpful, this gives you not only more armor and magic resist, it also gives you a second chance which when being relied on heavily to carry late game is a must and can be a game changer.

Magic Resist Boots - The only time I ever recommend these is if 4+ players are AP, otherwise, I do not really suggest them.

Thornmail - Great way to get the upper-hand against an AD team, especially when you are a bit behind, I suggest replacing either Guardian's Angel or Phantom's Dancers for these.

Maw of Malmortius - Great item against a team of AP, I suggest these for a match that has 4+ AP players, replace you Phantom's Dancers or Black Cleaver for these.

Infinity Edge - If you are carrying pretty well and the enemy team only has one tank for the most part, I recommend replacing you Black Cleavers for these, this way you can walk all over the enemy team.

The Mystic Shot and Essence Flux you want to upgrade evenly. These are your primary harasser source when in the lane. People ask me why I do not simply just upgrade the one all the way first then the other. My answer is simple, the Essence Flux you use when minions are in your way, therefore you want to get that to do as much damage as possible. The Mystic Shot is used to do heavy damage, so when the champion is exposed, you can deal damage quickly by upgrading this. My point is as long as you upgrade these two evenly, they go in hand and deal more damage together over time, than just upgrading the one before the other.

Cooldown Reduction - I personally like it just to get that ultimate of yours quicker or having a bit of an upper-hand, if you want a cheaper option, I recommend the Magic Resist Runes.

Armor - when in bottom lane against another ADC, these become rather helpful hugely early game, they are a must.

Attack Damage (Both Seals and Quintessence) - These are a must for an ADC Ezreal, gives you a great upper-hand early game and farming.

This page is still a work in progress. I apologize for not having much done, but I hope this helps everyone out. This is my first build I have ever posted, so please do not discriminate too much, still taking out the tweaks. :)