User blog comment:YourPrivateNightmare/The mystery of Blue Ezreal/@comment-10779726-20130612210358

Blue-Ezreal is play because of the ability to play safe while inflicting large amounts of damage to the enemy team. I'll explain the item choices as I go.

Ionian Boots of Lucidity

Gives you a hefty 15% CDR as well as a speed boost. Self-explanatory as it allows you to spam you Q with an ever lowering CD.

Spirit of the Lizard Elder:

Gives you the equivalent of a B.F. sword in pure AD, 10% CDR, an amazing harassment passive that procs with every Q you hit, and some nice regen for the laning phase. All for only about 450 more then a B.F. Sword.

Typically the item that people rush first. As for why people like it so much more, there's the effects I mentioned above, and the fact that if you get your core items faster, you snowball faster.

Manamune/Muramana

After Q spamming all day in lane you tend to run low on mana, thus a tear is in order, leading to a Manamune, buffing your AD and by the time late game swings around, massively increasing your mana pool and giving a nice buff to your Q damage/poke from the Muramana proc.

Typically kept as a tear until max stacks.

Iceborn Gauntlet

Gives you a whopping 20% CDR that allows you to again, spam Q all the more and apply a slowing effect in an AOE if it hits. The AP gained allows you to use your W and E to slightly greater effect as well as the +60 armor given letting you gain a good amount of survivability. Should be considered a core item as it allows you to kite indefinitely.

Bought as a Sheen after getting a tear, usually built straight into the Gauntlet ASAP. Note that it puts you barely over the CDR cap after upgrading into a Gauntlet.

Last Whisperer

For obvious reasons this is bought to increase your damage output, allowing your Q's to hit harder, assisting the penetration from both your other on-hit procs and letting your AA's do more as well.

Decide when you should buy this based on what the enemy team is building. (A.K.A. Buy it when they're stacking armor.)

Last Item

Situational, depending on the situation you can buy whatever your little heart desires.