Still a work in progress. Test out the build before commenting please. Guide about items, runes, and basically everything will be added soonish.

Every time Ezreal casts a spell and it makes contact with a target (Essence Flux affects friends and foes alike and both increase the passive) it increases his attack speed by 10% for 6 seconds. Stacks 5 times max.

The entirety of the build Ezreal's attack damage is decent, not super high like a pure AD build or the likes, but decent to make this passive always helpful for him. A quick way to full use it is to shoot your ultimate, Trueshot Barrage, at the enemy. Should always max out the stacks.

This will be your early game main damager. It has a ridiculously short cooldown, 6 seconds at level one before runes. It's a great method to last-hit minions that are too far away for you to basic attack, not to mention it does more damage.

Some advantages of this ability that aren't common among skills:
If you hit an enemy (Minion, Monster, or Champion), all your current cooldowns are reduced by 1.
If an ally of yours has Zeke's Harbinger and another has Will of the Ancients, both the Spell Vamp AND life steal activate on it.
It's a spammable high-damaging skill that both Ability Power and Attack Damage influence.

This...is probably your weakest skill, it has three useful things though.

1. Essence Flux will ignore all non-champions and can hit more than one.
2. Any enemy champion it hits alongside of taking some damage will also have their attack speeds slowed by 20/25/30/35/40% for 5 seconds.
3. Any ally champions it hits will have their attack speeds increased by 20/25/30/35/40% for 5 seconds.

((I have yet to confirm this, but I believe it is possible to buff Ezreal with this, it would take split second timing though. More word on this after I am able to confirm or deny this.))

A built-in flash with a ton of damage affiliated with it. This will be your most powerful skill besides Trueshot Barrage. This is a skill with many purposes.

1. Flash behind minions and use your skills to quickly take out the enemy champ.
2. Flash from the jungle to a turret to quickly take them down and then get out of turret range.
3. Flash into the jungle to escape.
4. Flash repeatedly to escape using Ghost and if needed the summoner spell Flash.

This is probably my favorite of all of Ezreal's skills.
It's range is global basically, you can shoot from one spawn point to the other hitting everything between. It does MASSIVE damage. There are really only three downsides, one of which can be mitigated by Ezreal's Mystic Shot.

1. It takes a second to charge. If used as a last ditch your enemy has the chance to finish you off or move before it fires.
2. Every enemy it hits reduces the damage taken from it by 8% down to a minimum of 30%.
3. It has a decently long cooldown.

Note: These are all before armor. I'll calculate damage at armor/magic resists 30, 50, 100, and 150 once I get the basic layout built and can find the numbers for the armor.

Level 7 Stats for Manamune, as that's likely for when you grab it.
Manamune:
1. 250 mana gained:
i. Mystic shot does 185.84 damage.
ii. Essence Flux does 82.54 damage.
iii. Arcane Shift does 78.15 damage.
iv. Trueshot Barrage does 400.78 damage.
2. 500 mana gained:
i. Mystic Shot does 190.84 damage.
ii. Essence Flux does 82.54 damage.
ii. Arcane Shift does 78.15 damage.
iv. Trueshot Barrage does 405.78 damage.
3. 1000 mana gained:
i. Mystic Shot does 228.84 damage.
ii. Essence Flux does 82.54 damage.
iii. Arcane Shift does 78.15 damage.
iv. Trueshot Barrage does 418.78 damage.
Level 12 Stats, as it's likely for when you grab this.
Bloodthirster(#1):
Full stacks:
1. Mystic Shot does 369.44 damage.
2. Essence Flux does 84.32 damage.
3. Arcane Shift does 230.4 damage.
4. Trueshot Barrage does 676.48 damage.
Level 16 Stats.
Rabbadon's Deathcap:
1. Mystic Shot does 426.796 damage.
2. Essence Flux does 308.388 damage.
3. Arcane Shift does 435.485 damage.
4. Trueshot Barrage does 1016.582 damage.
Level 18 Stats from here on out.
Bloodthirster(#2):
1. Mystic Shot does 535.108 damage.
2. Essence Flux does 409.324 damage.
3. Arcane Shift does 436.655 damage.
4. Trueshot Barrage does 1119.986 damage.
Archangel's Staff:
1. Mystic Shot does 604.409 damage.
2. Essence Flux does 533.227 damage.
3. Arcane Shift does 591.53375 damage.
4. Trueshot Barrage does 1333.8405 damage.

I chose these runes for good reason.

Marks of Insight so that your spells pack more of a punch as they break through some magic resist.
Glyphs of Focus so that you can spam your skills more freely and get that ult down and ready to use as quickly as possible.
Seals of Vitality to help counter Ezreal's extreme squishiness.
Quintessences of Desolation to get Mystic Shot and his basic attacks through some armor.

Changing Quints and Marks around isn't a bad idea, I just found this combo to be best. Seals of Clarity are viable, as well.

I chose the standard set for casters of 9/0/21. (I know Ezreal isn't technically a mage, however, most of his damage comes from his abilities so I'm calling him a caster)

Note: For those who are NOT level 30 yet and only can grab some of the masteries, here are my suggestions in order.

Archmage's Savvy: 3/3
Ghost: 1/1
Good Hands: 3/3
Awareness: 4/4
Sorcery: 4/4
Archaic Knowledge: 1/1
Perseverance: 1/3
Utility Master: 2/2
Greed: 1/1
Expanded Mind: 1/4
Quickness: 3/3
Intelligence: 3/3
Blink of an Eye: 1/1
Presence of the Master: 1/1

Viable changes would be moving Greed around, to most any of them in the utility tree.
If you choose to take Clairovoyance to make sniping shots easier, moving the point from there to Mystical Vision.

I start it off with Boots of Speed and 3 health potions as Ez is really squishy and he needs the move speed, also, this build is based around Ezreal being mid so he needs to be fast to harass well and avoid being harassed, otherwise it's just a slaughter.

I give him then Tear of Goddess to get the first part of Manamune done and to start fueling his mana pool which in the beginning is too small. He then gets his Ionian Boots of Lucidity to give him a bit of CDR. Finishing off Manamune he moves on to Bloodthirster. That gives a ton of life steal and attack damage. Next, he gets Rabbadon's Deathcap to empower all of his abilities. Topping it off with Archangel's Staff to give him an even larger mana pool and to get AP from it.

*****IMPORTANT NOTE TO GET MAXIMUM AP POSSIBLE: Make sure that you have ALL the mana you can get from Manamune.*****

Banshee's Veil:
When they have either a lot of AP, a champ like Karthus with his global ultimate, or just lots of CC.

Hexdrinker:
Same as with Banshee's, just it's more and less better. (Less nuke stopping, but higher chance of saving your life)

Mejai's Soul Stealer/Sword of the Occult: ONLY if you are getting fed. ONLY. You are not someone like Karma or Sona who get tons of Assists with few deaths.

Mercury Treads:
For those heavy AP/CC teams.

Rylai's Crystal Scepter:
Gives a bit of CC, can be handy. Along with some health and AP. Personally I wouldn't grab it, but it's a good choice for many.

Guardian Angel: If you're just getting focused constantly before anyone on your team can do anything.

Quicksilver Sash: For heavy CC teams.

Guinsoo's Rageblade: The AP boost is a bit nice, but there are better items, your choice on this.

Hextech Gunblade: It's an expensive item, but it's worth it if you're getting tons of kills/assists and would like to be able to stay in lane longer or just a quick jungle instead of having to completely recall.

Voidstaff: If they're building lots of Magic Resist.

Sheen > Trinity Force: For when you'll be spamming auto-attacks to make your attacks hit that much harder.

Randuin's Omen: You are getting focused so much and it's mostly/entirely AD. Otherwise it's pointless.

Alternatively, Thornmail. Gives more armor, and for the auto-attack champs like Ashe and Xin Zhao this can be very brutal.

Force of Nature: You are getting focused a ton and it's mostly/entirely AP. Otherwise it's useless.

((I actually didn't copy and paste most of that, I typed it all out. Go quick typing speed, go!))

Warmog's: This is a very, very expensive item that can be dealt with better and Ez isn't meant to tank or anything like that. If anything he needs armor/magic resist. NOT health.

Lich Bane: He doesn't have much AP for this to be too helpful, and all of his skill shots except for Arcane Shift are out of the range. Getting in range to use this is just asking for it.

Sunfire Cape: No...just no.

Thornmail: The armor is nice, and the passive is a bit helpful, but you shouldn't need this. Best to stay out of range.

If going Mid, grab boots first, if you're going a side line, grab Meki Pendant and some pots.
Handy Tricks that Ezreal can do with his skills.

Bush Checking: Arcane Shift, if there are no minions around, use it next to a bush and it will attack a champ if there is one in them. Alternatively, shoot off Essence Flux and you can see exactly how many are in there, I'd suggest Arcane Shifting away if there are at least 2. Mystic Shot works well, too. It only tells if there is one, though.

If you grabbed Flash: Someone with low health near a turret but you can't quite finish them off just from shooting from the jungle with Mystic Shot/Essence Flux. Shoot those two off, do a quick Arcane Shift in and then Flash back into the jungle. If all went well you just killed them without even getting hit by the turret.

Team Fights: Don't be greedy. Fire off your ult at the beginning when they're all clustered. They'll all be weakened severely and you can still score some kills with fast Mystic Shots and Essence Fluxes while they all die and only one or two, if that many of your team dies.

Sniping: Ezreal is one of the best in the sniping department. NOT EVEN CAITLYN WHO IS A SNIPER CAN SNIPE THIS FAR. Ashe can, but her attack can be blocked. Tell your team ahead of time to announce sniping possibilities. If you grabbed Clairvoyance, this would be a good time to pop it, don't fire immediately, sometimes they'll move out of the way if they see. Wait like two seconds. If they're already recalling, fire immediately. For sniping, make sure to aim with a click, not just smartcast it.

Smartcast, it makes Ezreal OP. You can get your entire 5.4k (Including 3 auto-attacks) damage before armor out in roughly 3 seconds.

5/18/2011: Created Build.
5/25/2011: Changed the name of "Situational Items" to "Items to Consider." Changed the name of "Items you shouldn't get, but the situation calls for it" to "Situational Items".
Added Thornmail to the Situational items section

I haven't been able to extensively test this out yet. (Never made it past the first Bloodthirster's), however, it works well.