I have played as Ezreal for a while now and mostly used a standard AD only build. However after switching my main to a Twisted Fate using a build that benefits from both AP and AD, I tried to build Ezreal under that same premise such that your main skillshot nuke does a TON of damage with reasonable survivability.

There are of course many ways of building him I have listed here the build order for my last two games I have played and listed some alternate items and runes you could take instead.

I play quite cautiously at first skirmishing the opponents until seeing an opportunity for Arcane Shift to hit your opponent and line you up perfectly for a fast paced auto attack, and your 2 skill shot combo which picks of people with ease. At early game this can do about 70% of your targets health in one go with the APen and MPen runes and masteries.

Hope you enjoy it!

I originally started with full APen / AD runes and quints but quickly found out that the health helps so much early game that I swapped runes.

The APen and MPen also is great in both early and late game situations. At the start you can do a considerable amount of damage easily with your skillshot and autoattacks.

Armor I chose as my main problem was playing vs melee characters that loved to stun and slow (e.g. trundle or nunu) and this seemed to make a considerable difference.

XP and the Gold/5 Mastery in Utility for faster leveling for easier mid-late game carry dominance. The build does require several expensive items so the gold/5 is a good addition to have for this specific build.

Masteries in Offense have to include the MPen and APen as your main skillshot uses both modifiers when applying damage. The other damage masteries are pretty standard.

Sometimes it is best to get Sheen before the Vamp Scepter even though this is only one item change it can make a differenece.

Early Occult/Mejais does mean you will be wanting to get involved heavy in ganks at low level, taking flash/ghost with Arcane Shift gives you good escape tools so your bonus isnt lost.

There are alternate items that may also be a good choice, for example Hexatech Revolver -> Gunblade can be a good addition depending on the circumstances and Banshees Veil is another obvious addition to the build

I took Flash as it works both for escape and for chasing down fleeing enemies, whilst Ignite helps you get early fast kills. As soon as you hit level 2 a well timed auto attack, ignite, shift/eldritch can easily take down most champions that are not on full HP.

Other good alterantives would be Ghost for escape/chase or recall to keep your downtime to the minimum.

First guide I posted, feel free to criticize I have played lots of Ezreal builds but this one works best for my playstyle! I will edit this guide soon and make it tidier!

I hope you enjoy playing this build, skirmishing up to level 6-8 then breaking out and bringing on the pain seems to be my "tactic" and this character seems to be the best at it!

Any comments welcome :-)

Pros:
Very high bust damage
Great harrasment
Good abilities to escape
Good abilities to position your skillshot
Good abilities to chase down opponents
Very good carry

Cons:
Not very high HP
Dying when you have stacked Mejais/Occult can really lower your DPS busrt
Low mana early game