As a champion that has been known to abuse alot of items Ezreal has a varierty of items that he could build. Due to his jack of all trades nature Ezreal usually builds from alot of diffrent champion classes. In this section i will go over the most common built items for the current meta.
Manamune
Manamune has been a core item on Ezreal for a very long time. It provides you with a lot of stats you want like Ability haste, Damage and it stacks Mana on abilities. However this item truly shines once it transforms into Muramana which is Ezreal's biggest midgame powerspike as it gives him more damage per ability with its passive. This enables Ezreal to suddenly deal alot more damage per Mystic Shot which is you main dps ability. Manamune is an excellent second item since you would stack tear while purchasing Trinity Force/ Essence Reaver. Overall its pretty much just a solid item for Ezreal so you would rarely not buy it regardless of build
Trinity Force
One of Ezreal's iconic items. Trinity Force is mainly due to it's spellblade effect which gives Ezreal more damage on his Mystic Shots. The main diffrencce between Trinity Force and Essence Reaver is mainly the fact that trinity give hp which makes Ezreal more durable and attack speed which makes kiting easier. In season 14 however it has lost alot of the power it had as a mythic item and Essence Reaver is generally speaking better due to its damage. Still viable into heavy dive comps where you need that extra hp to survive imo
Spear of Shojin
A new item you can build in season 14. Spear of Shojin usability mainly comes down to the fact that its two passives are extremly good for Ezreal. The first passive, Dragonforce, gives you 15 cooldown reduction for all your basic abilities . The second passive, Dragon will, gives you increased ability damage for every ability you hit stacking up to 4 times for 12% damage increase which helps you deal with armor stacking Tanks as it amps your Essence Flux which deals magic damage. In that sense its similar to the reason why season 13 Trinity Force was strong. It's baseline stats ain't to bad either. It gives pretty decent ad and hp gives you the durability you lack from not building Trinity Force. In other words this item gives you basically everything you need so you should be buying it in every single game.
Serylda's Grudge
Serylda's is a relativly new item on Ezreal and serves as one of the two options Ezreal has for armor pen item. While Serylda isn't as good as Lord Dominik's Regards when you account purely for damage its built more for its utility and lethality. Seryldas passive allows you to slows enemy champions whenever they are below 50% hp. This means that for every Mystic Shot you hit the next one becomes alot easier. It also gives Ezreal more chase and kiting power while also helping him deal better with armor stacking tanks. Therefore Serylda could also be considerd a core item for Ezreal as it fits nicely with his champions playstyle . Due to the changes in season 14 however going Lord Dominik's Regards is usually more viable than Serylda. Only pick this up if the enemy has no tanks as it's still better than Lord Dominik's Regards vs squishys
Ravenous Hydra
Ravenous Hydra has alot of the stats Ezreal want. However like most items mentioned you usually buy it due to it's passive. The passive of Ravenous Hydra gives auto attack and spells aoe damage. Ravenous Hydra's passive enables Ezreal to go from one of the worst among marksmen in terms of waveclear to being on par with most of them. The lifesteal is also pretty nice incase they have poke heavy comp like Xerath or Lux.In general the item is solid but not as core as Manamune and Serylda's Grudge and can be swapped with some of the others on this list. Season 14 made this more of a gimmick item on Ezreal so only build it for fun
Blade of the Ruined king
Blade of the Ruined King is a very situational item on Ezreal. What makes Blade of the Ruined King good is its passive which gives extra damage against High HP individuals which mainly consist Tanks and Juggernauts. The attack speed the item gives is not super useful, but it feels nicer to farm with it and lifesteal + damage is always good. Blade of the Ruined King is as previously mentioned a pretty niche item as you'll only really be bulding it against very heavy tank comps, or if they stack alot of hp. You'll usually be building it 4th or 5th but can be built 3rd if they haven't
Black Cleaver
Black Cleaver is another Fighter item which Ezreal can buy. Passivly the item shreds armor from the enemy target through dealing physical damage which in Ezreal's case is his Auto Attack and Mystic Shot. Its raw stats aren't too bad either giving both AD and AH which is good. HP is an okay stat on Ezreal as it gives you more survivability. Due to Black Cleaver's passive you'll be mainly building vs armor stacking teams. This means if you're fighting Malphite or Rammus then Black Cleaver will be infinitly better than Blade of the Ruined King. Generally you should be building Black Cleaver more often than Blade of the Ruined King so if you're unsure, build Black Cleaver.
Frozen Heart
Frozen Heart is one of the most consistent defensive items Ezreal has been able to build. It's mainly used against teams that are heavy ad or have a fed ad champion. Frozen Heart's passive reduces both damage from AA and reduces attack speed in your vicinity. Now the reason why Ezreal uses this item while most marksmen insteed opt in for Guardian Angel is because it both gives mana which empowers your Muramana procs and damage and it gives you ability haste. Frozen Heart then has a very clear purpose. If you are facing alot of marksmen, Slayer and full ad comps then this item allows you to survive alot longer in teamfights. Usually i would slot this 4th or 5th item depending on how fed i am and how likely the enemy teams Slayer is going to one shot me.
Maw of Malmortius
Maw of Malmortius serves as Ezreal's main defensive option against ap burst. Its passive gives you a magic shield after you drop to 30% hp which soaks some of the ap burst damage and once popped it also gives you lifesteal which you can use to gain back alot of the lost hp. Maw of Malmortius stats are also pretty good, it gives ad,ability hate and magic resist all of them being good on Ezreal. Like Frozen Heart it's situational item but instead of against ad you build vs ap burst. This means it's very good vs champs like LeBlanc or Syndra and in general the Mage class who ofte have the ability to one shot you with one spell rotation and full ap comps. Should usually be bought 4th or 5th
Guardian Angel
Guardian Angel is one of the more built defensive options for Ezreal its passive is what you mainly buy it for due to its ability to revive you in the middle of a teamfight. The stats from Guardian Angel isn't the greatest, you'll be mainly building this due to its passive in some cases you should even sell it to get Frozen Heart while you wait for it to get back on cooldown. The main use for Guardian Angel is therefore to survive unlivable burst like Zed/ Rengar or even to bait Slayer's to pop it in exchange for their ult cooldowns. It also usually deters enemy players from targeting you in teamfights due to the fact that you can potentially win teamfights from just getting them to waste cooldown. I would recommend getting this if they have a comp that requires getting picks before a teamfight to win. Usually slotted 4th or 5th
Silvermere Dawn
Silvermere Dawn is another defensive magic resist item. Like most items the passive in this case is the most important part of it as it hase the ability to remove supression and in general cc. The stats ain't too bad but no great on Ezreal. It gives both ad and mr with some hp to spare. The main reason you're buying this is if you're up against someone with suppression like Malzahar or Mordekaiser ult. The other reason you'll be buying this is if they have alot of cc like for example Leona, Ashe botlane combo. All in all a decent defensive item but extremly specific.