Personally, I have Ezreal as a "pocket pick," even though you spend a long time quite weak due to the tear rush, if you can get to a triforce quickly then your damage just explodes. And you continue to scale hitting power spike after power spike, as your damage ramps up exponentially with each item, Triforce, Muramana, Blade of the Ruined King, are all big boosts to your damage as opposed to the normal story on ADC where you need 2-3 items added together before you can really start deleting people, with Ezreal your damage curve is immediately at the top as soon as you get a triforce, and each subsequent item just keeps that damage curve capped.

His main weakness is his waveclear and he can't take towers as quickly as other ADCs and in some respects his teamfight isn't as good, lacking sustained multi-target damage and any form of CC. Blue build allows his Qs to do frankly obscene amounts of damage if you hit an enemy champion, but his base damage against minions, towers, dragons, baron, etc leaves a lot to be desired.