HI
This is my first build and I am featuring Ezreal after the release of his amazing Pulsefire Skin.
You may find some peculiar items and believe this build to be mediocre but I asure you that it has been tried and tested in many different comps and the outcome is usualy the same... Flawless Victory!
I play Ezreal as an AD Caster, this means I rely very much on his abilities in order to dish out tons of damage. This also means my build is a far cry from what a normal carry should build. I reaize some people like to play EZ full carry and I very much support the "damage first" policy, but my question would be: "Why play Ezreal as a carry when there are so many better pure carrys out there". Sure he is fun to play but I have found him to be quite poor in fights compared to other carrys such as Ashe, Vayne or Caitlyn if you only rely on autoattaks to get the job done.
So stay a while and listen, try the build and see what gives.
Oh and thanks for leaving constuctive comments as this is my first guide I would love some feedback.

I take as much Armor Penetration as I can with runes.
Some say Ezreal has low lategame damage... well this will help a great deal, add your runes to your masteries and Items in the build and you'll be shreding that armor in no time.

I take very unusual masteries as I try to get as much damage as possible keeping in mind that I play a Caster. In he end I just take mana in utility making mana consumtion less of a strain (also adds to the damage of Manamune).

Here comes the interesting part. I start off with Boots and 3 Health Potion. This gives me sustain and a good poking ability. Sheen is a must have for Ezreal if you play him as a Caster and it then build into Trinity Force (a very expensive Item I build ONLY on Ezreal, Corki and Nasus), the bonus damage on every Mystic Shot is Outrageous! Truly, truly, truly...
Now for the only real Item that may have some of you thinking i'm totaly crakers.
Youmuu's Ghostblade is a grat item for melee characters such as Master Yi or Olaf, but is it realy intereting on a carry? well the answer is no, not realy, the active is maintaned longer with every melee attacks so a ranged caster would only have 4 seconds of the effect. Well after many trials and errors I have found that whichever way I look at it I love, LOVE! Armor Penetration. It makes so much difference for a Caster, as you don't get as many hits on a target as a normal carry would do you want those few hits to blow you're enemy's head off! Anyway I build The Brutalizer befor finishing trinity and just befor geting Tear of the Goddess. As far as mana is concerned, you need a lot of it to play as a Caster, and if you don't have a Soraka as support then you need to get your Tear of the godess early on as sugested in my build. The rest of the build is self explanatory. I get Bloodthirster befor Infinity Edge so as to give me good sustain in fights and get those staks up early. If you don't like keeping the Youmuu's Ghostblade in a long game you can swap it for a Black Cleaver or Madred's Bloodrazor

I take Heal beause I am a carry, period... and Ghost because Ezreal allready has a build in Flash. Ghoste also synergizes well with Youmuu's Ghostblade active.

PROS
-Great fun to play
-Great damage with this build
-Not too expensive to build up this way and great Dmg/gold ratio
-Good esacpe/chase tool ( Arcane Shift)
-Smartcast is MADE for this character!
- Essence Flux usefull for downing turrets when targetting alies with the speedbuff.
-Now 100% manly with the new Pulsefire Skin
-Does not require a map.

Cons
-Must keep an eye on mana use if not laning with Soraka
-Squishy early game (come on guys I always see this in guides but seriously... who isn't squishy early game?)
-Squishy late game (he's not a frinking tank ofc he is squishy :P)
-Good AP ratio on his spells (you might want to play him ap...)
-Only Mystic Shot deals Physical damage (so I take magic pen in masteries for extra damage on other spells)
-Ult can be doged if enemies see you casting it (hide in bush or out of minion range for full suprise!)
-Escaping with Arcane Shift onto dragon or nashor if low health will KILL YOU:P
-Your damage will be lower than you opponent's until you get your The Brutalizer, don't worry, be patient and if you really want damage early then swap my Armor Peretration runes for AD (not as good late game)

Good use of your Mystic Shot can land you last hits you would have otherwise missed.
Trueshot Barrage can be used to clear minion waves.
Essence Flux does not hit creeps :(

In teamfights stay back and land as many Essence Flux/ Mystic Shot as possible, laungh Trueshot Barrage either at the first engage or when enemies get low on health. As soon as a target gets low and is open for focus, arcane shift onto them and folow up with Essence Flux/ Mystic Shot then finish them off with basic attacks. Always use your basic attacks when your Mysic shot is on CD but use the ability EVERY time it becomes available. Cooldown on Mystic shot will not be very high with the 19% reduction from masteries and Youmuu's Ghostblade (don't forget to activate Youmuu's Ghostblade in teamfights). I try not to use Arcane Shift if possible and keep it as a means of escape but if you are clearly winning the fight don't worry about it and if the worst comes to the worst use your Ghost to flee the battle.

I love playing Ezreal, I have grown quite fond of this build which is why I am sharing it. Keep in mind this is my first guide and I will take comments and sugestions into consideration to help make it better but please remember this is a guide for a PHYSICAL CASTER Ezreal and not at all pure Attack Damage. I hope you find this guide helpfull and usefull in your battles through the fields of justice.