Ezreal is by far my favorite champion to play. He can play many different roles. In this guide I cover how I play him as an AD carry and as well as playing him as AP mid. PLEASE DON'T DOWN VOTE MY GUIDE FOR THE AD ITEMS, SORRY FOR MAKING YOU READ BUT I EXPLAIN LATER. Remember this is how I play, if you don't like it then don't do it. Please try this guide before you vote on it.

Please do not troll me for bring heal and teleport.

Heal-Great for staying alive. People will dive if they think they can get you,this is when you use your noob heal to turn things around.

Teleport- I prefer to bring this for multiple reasons. Early its great to help with ganks or go back and get an item and be right back without missing anything.

Exhaust/ Ignite are my second choices. They are obvious huge slow and damage.

Flash-I hate this spell on Ez. I know most people like it but Ez already has a flash. I don't think he need a second.

I don't see the point in any other spells other than either Surge for AP or Ghost if you prefer that.

Pros:
Great Harass
Build in Escape
Long Range Ult
Decent amount of damage
low cool down

Cons:
Squishy
No cc
Not a crit champ like other carries

I bring armor and magic resist because I believe it helps carries very well. I am usually way more tanky than the carry i go against and therefore can survive better. Also the armor pen marks are just a standard rune for any of my ad champions.

Anytime I play AD Ez I start with a Doran's Blade. It's provides bonus health and damage early. Get Boots next so you can run or chase depending on the situation. The next item is a Wriggle's Lantern. This is an amazing early game item. You get the damage, armor, and life steal. As well as a free ward. Next build a Trinity Force. This item works wonders on Ezreal. Every bonus helps him in some way. The Sheen in it works great after all of his skill shots. After this point I build based on the situation. If the enemy team is ap heavy get a Hexdrinker or a Banshee's Veil or both. If they are AD heavy build armor like a Frozen Heart. If you team isn't do enough damage get an Infinity's Edge or a Bloodthirster and other ad items. I recommend a Banshee's Veil regardless because it is a great defensive item. If you are new to Ezreal or bad at skill shots think about a Manamune. It gives you a ton of mana and some damage as well to practice on Ez.

For AD Ez Mystic Shot is your best friend. It's cheap, has a low cool down, and does a ton of damage. It has a 1.0 scale for ad so it does all of your attack damage as bonus damage. It also applies on hit effects like sheen.

Arcane Shift is a great utility spell. It gives Ezreal his own teleport as well as damage.
Use this ability to harass with your other skill shots. However be careful not to get to overextended. It takes a lot of mana so not using it is also an option. Just keep it for when you need to run from a gank or are being pushed hard.

Essence Flux I think is not effective when going ad. It takes a lot of mana and gets its bonus from ap so I rarely get it or use it early.

Trueshot Barrage has many uses. For those of you who play Ashe it is a similar ult but it has I believe more uses. Barrage can be used to hit anything on the map from anywhere. However if your using it to kill make sure to use it so you wont hit to much before your target because each target hit reduces the damage for the next one.
I use this ult to:
Finish a fleeing enemy.
Initiate or End a team fight.(When a team is all going for one turret, it can be used to hit all of them and wipe the minion waves,it will scare most people.
If you time it right you can steal baron or dragon.
The Ult scales great going either ap or ad so it will do a tone of damage either way.

Pros:
Great Harass
Build in Escape
Long Range Ult|
High Damage
low cool down

Cons:
Squishy
No cc
mana problems early

AP Carry Runes:
I bring almost the same runes, however I focus on magic resist more as I usually mid ap.
I also bring Ap quints and magic resist marks to go with the AP build.

For Ap start with the Meki Pendant and health pots. Get boots of speed next. Then get a Fiendish Codex. It provides mana regen, ability power, and cooldown reduction. Next finish your boots with the sorcerer's boots. The finish Morrelo's Evil Tome. Next I prefer to get a Will of the Ancients for its ability power and spell vamp. Then I prefer the Rylai's Crystal Scepter. It gives you a nice health boost, ability power, and a nice slow form your skill shots. The rest of the items are situation based, but I prefer a Deathcap and Scepter for AP and magic resist.

Mystic Shot is a great damage and harass skill for AP Ez but not his main damage output.

Arcane Shift is a great utility spell. It gives Ezreal his own teleport as well as damage.
Use this ability to harass with your other skill shots. However be careful not to get to overextended. It takes a lot of mana so not using it is also an option. Just keep it for when you need to run from a gank or are being pushed hard.

Essence Flux This is your most effective damage spell. It does a ton of damage and has a great AP ratio for a ranged attack. Also this spell only targets champions and does full damage to any that it hits. This makes it great for mid because the enemy can not hide behind the minion waves. Also in team fights if you get low on mana, focus this ability on your AD carry or the enemy AD carry. It will either give your ally attack speed or reduce the enemies attack speed.

Trueshot Barrage has many uses. For those of you who play Ashe it is a similar ult but it has I believe more uses. Barrage can be used to hit anything on the map from anywhere. However if your using it to kill make sure to use it so you wont hit to much before your target because each target hit reduces the damage for the next one.
I use this ult to:
Finish a fleeing enemy.
Initiate or End a team fight.(When a team is all going for one turret, it can be used to hit all of them and wipe the minion waves,it will scare most people.
If you time it right you can steal baron or dragon.
The Ult scales great going either ap or ad so it will do a tone of damage either way.

Regardless of what lane or type your in,early just go for last hits. Do Not push your lane to far unless you know you can kill the enemy champions and can escape a gank easily. For AD when you get a Wriggle's Lantern kill minions to your hearts content.

Overall Ezreal is a great ranged champ for AP or AD players. He has Great damage, harass and carries really well. Regardless of how you play he works for either type, however I have not found a hybrid Ezreal that is good enough to compete. If you have any suggestions please let me know. This is my first guide and I would like to see what everyone thinks.