Hey folks
First of all forgive me for my poor English. I have played with master yi more than 1000 times and this build reflect all those experience! ;)
I had more than 100 Penta kills and almost 300 Quadra kills. So be relax and just follow the built. In my view, master yi is the greatest champion for late game. Just give him some space and see what he can do.
I should say in S6 with new itemization, he is even stronger than before.
Master yi is a pure AD assassin. he is neither TANK nor AP (forget about AP master yi, he is gone:)).Never waste your money by building a tank or AP set for him cause these sets do not scale up with his abilities.

+ Probably the strongest 1vs1 champion late game.
+ Easy Penta and Quadra kills
+ Strong farmer
+ Refreshable abilities
+ High base movement speed

- Weak in ganking due to lack of crowd controls
- Highly vulnerable to stuns
- Weak in early game encounters

This built is highly dependent on your runes and masteries since you don't have any boots. So please buy the aforementioned runes and set the same masteries to make up that movement speed. there will be no single feature of an item that can be useless for you. so basically you use all your money in the most efficient way (no waste). And this makes you much stronger since you are replacing the boots with another strong item.

+ highest output damage (almost 1300 per each basic attack in full set): due to 100% critical chance, your damage out put is crazy. Imaging in late game your attack speed is 2 while R is active, so basically in 2 seconds you will make 4 hits, each hit 1300 so in total 5200 damage dealt. for each hit you gain almost 40% of the damage dealt as life steal. so you get 2080 heath back in 2 seconds which is almost your whole bar of health.
Math calculation: 111 (basic damage) + [70 (reaver) + 80 (Death's Dance) + 70 (Infinity Edge) + 80 (Ravenous Hydra) + 30 (Elixir of Wrath)]*1.1(wuju style passive) = 485
Now adding fully stacked bounty hunter (+5% damage) and double edged sword (+3% damage) amplify your damage to 500. At this point your basic attacks make 1200 due to crits. However, for champions below 40% health, the output will be 1300
Having a Barron buff and elder dragon can make this even higher.

+ sufficient movement speed without boots: you don't need to be worry for movement speed since this build will provide you 415 flat movement speed in the game without boots, your Highlander, dragon buff or taking the phantom dancer's passive into account. It all comes from runes, masteries, other items, and basic movement speed. It can be more intensify when you get the third dragon buff. Plus due to 40% reduction your R will be ready every 45 second and for chasing the enemy. Even without R your speed will be enough fast by phantom dancer passive (480).

+ highest cool down reduction: this can enable you to get most out of your Q and R which are your essential abilities.

+ huge amount of AOE damage: because of your Q in team fight you make a output damage of 3200 (800 total damage of Q in late game and up to 4 enemy). In addition, due to stattik shiv your first basic attack in team can make additional 1250 damage (100*2.5*5). At the end, Ravenous Hydra makes so much AOE damage in team fights that no one will get close to u. :)

- No armor or magic resist item: maybe the only cons of this built are that you have no armor or magic resist. Thus, in team fights if they catch you before you use Q, you may die (So in team fights don't go first) and you will be weak in early game (thus, avoid 1vs1 fights until level 11).

Stalker's Blade - Bloodrazor: a substitution for stalker's blade - devourer, however it is not as powerful as stalker's blade - devourer. Nevertheless, we need this item early game for farming and its attack speed.

Essence Reaver: really useful item. always buy this item since it has a great synergy with other critical strike items and boost your cool down reduction to 30% after buying 30% critical chance (not sure exactly). Plus, it will obviate your need for mana which is crucial for you to perform consecutive Alpha Strike. it works perfectly with your Alpha Strike and your passive since both can critically strike and provide you mana. on top of that, it gives great amount of AD. I love this item:).

Death's Dance: this item makes you enable not only gain health back from your basic attack, but also from your Q Alpha Strike. To make it more clear, imagine in late game with full set, you gain more than 500 health back by each Q Alpha Strike in team fights, so basically after 2 consecutive Alpha Strike you gain almost half of your health and while your opponents lost more than half of their health :). The second passive of this item may not look appealing but believe it or not it will let you stay alive longer and give this opportunity to rescue yourself after fight by using your Meditate or letting other allies heal you.

Infinity Edge: provides you enough AD. In addition, makes your critical strikes more powerful. you make the most use out of this item since all your hits considered as critical strike.

Phantom Dancer: As you know it increase your attack speed, your crit chance, and your movement speed greatly. It also helps you to chase your victims much more easier by boosting movement speed and ignoring units collision:). But the most interesting part is Lament which makes you take 12% less damage for 10 second in 1vs1 fights which enhance your chance of victory.

Statikk Shiv: You make the most use out of this item since all your basic attacks are critical your passive makes 250 damage to each enemy in fight which means 1250 in total. Plus, it provides a portion of your movement speed. (no need to mention how useful it is for farming:)) NOTE: you can sell the shoes right after buying this item.

Ravenous Hydra: this item becomes so crazy in team fight against enemy team members. Your late AD state in the game is around 400 to 500. While the passive part of this item is always on, every time that you use the active part it makes huge amount of damage that leaves no way for your opponents except run. (no need to mention about the amount of health you gain back in the team fight that makes u almost immortal)--{if your r really not happy with this item, just keep the jungle item or buy the "blade of the ruined king".}

0- Hunter's Potion: upgrade your health potion as soon as you can. the potion can completely obviate your need for mana in early game since by killing one large monster you will one charge of it.

1- Stalker's Blade - Bloodrazor:

get this first.

2- Boots:

buy these boots and keep it until mid game. As long as you can upgrade other items with no difficulty keep these boots. Once you find it hard to update other items due to less space sell them. However, I would suggest you to sell them only if you have already bought the Statikk Shiv.

3- Essence Reaver:

get this as your first luxurious item. This has to be second so it can boost your cool down reduction and obviate your need for mana.

4- Statikk Shiv:

buy this right after Essence Reaver to boost your cool down reduction and also prepare yourself for selling the shoes.

5- Death's Dance:

now it is time to build some life steal. Get this one as your next item.

6- Infinity Edge:

now it is time for this precious item. :)

7- Phantom Dancer:

buy this one as your last item. You can also change the order of buying this item with Statikk Shiv.

At the end, when it is heavy team fights i would suggest to substitute Stalker's Blade - Devourer with Ravenous Hydra.

Double Strike: will benefit from your critical strikes since it applies all on hit effect. Thanks to new update the second strike will automatically search for enemies if first strike kills a unit.

Alpha Strike: will also benefit from your critical strikes since it can critically strike. Plus you can use it almost every 8 seconds due to your 40% cool down reduction and since your attack speed is high with using basic attack you can lower the cool down extremely. It also scales up very well with high amount of your AD.

Meditate: does not scale up in terms of the amount of health you get from it but you can use it more often thanks to 40% cool down reduction(almost every 20 second instead of 35 second). Now it can be used more efficiently against some champions like tryn since it stores double strike stacks.

Wuju Style: scales up very well with your high AD and can be use more often. It also benefits from your attack speed which enables you to make more true hits while wuju is active.

Highlander: it can be used every 45 second!!! also scales up with your numerous kills and assists! :)

NOTE: one might argue that the best way to scale up the Double Strike, Alpha Strike and Wuju Style is to increase the attack speed. I am not against that and I also tried to maximize it in my build with small different that I balanced between your AS and AD. The current build may not provide that much attack speed by its own but the point is your gaining additional from your R. Highlander can boost your AS so much that it can completely obviate your need for that many AS items. And as I mentioned before your Highlander will available every 45 second which means you can use it every minute in the game. So I tried to make the balance by increasing the AD, cool down reduction and sufficient AS.

Warlord's Bloodlust : restore health equal to 3-40% total attack damage (at levels 1-18) and grant 30% movement speed for 0.75 seconds. And can critically heal which means lots of health back. 0.4*1200 = 480, very well matched with this build!

Dangerous Game : is also very useful your keep you alive longer while you are in team fights by restoring 5% of your missing health.

Wanderer is also great by increasing your movement speed by 3%.

the only point here is that you MUST buy the Greater Quints for movement speed. No question. :)
About marks you can choose between Mark of Critical Damage and mark of armor penetration. The first one can make you much more stronger late game however it may have a weak early game. The latter is visa versa.
For seals and glyphs I would suggest you to go for armor and magic resist to make almost the most use out of them.
NOTE: one might say that now that we are aiming for 100% crit chance, lets buy all the runes (except Quints) for increasing crit damage. I won't agree with that even though it makes your late game crazy. Because your early game will be much more harder this way and you may even lose the game before you get close to mid game. However, if you are sure about your early game then change everything to crit damage. :)

Never go into the fight as the first person. your job is to hide somewhere, wait until your teammates do the damage and then when enemies reached to their one third health or half, jump in and finish those ADC and AP champions who are low but still making lots of damage from a far distance.
Always use your Q on the lowest enemy champion, never waste it on tanks for the first use. You must get a kill after Q and 1 or 2 auto attacks. Once u get the first kill your Q is there again and you can use it again in team fight. Every time you land your Q, the rest of enemies who are not low will lose a portion of their health until it comes to their turn :)). You can use it sometimes for 5 times in a row if you use it correctly.
Morgana can be a perfect match for you. Once she put her shield on you, you can just go in with no fear.

lets see what you get at the end from this build (only from items, runes and masteries):

Attack damage: 80 + 70 + 70 + 80 + 30 = 330
Attack speed: 35% + 45% + 50% = 130% (with jungle item)
Life steal: 15% + 12% + 20% + 15% = 62% (with warlord's bloodlust)
Critical strike chance: 100%
Cool down reduction: 40%
Movement speed: 415 (roughly)

So basically with initial stats of the champion and masteries, your AD should reach close to 500 and AS up to 2.

14/12/2015: adding purchasing order chapter.
24/12/2015: adding description for jungle item and health potion.
20/01/2016: adjusting the build with new update for items and masteries.
20/01/2016: GAME UPDATE
12/04/2016: adjusting the build with new update for items and masteries.

Warlord's Bloodlust AS now increased from 20% to 30% and its life steal from critical strikes has been changed from 15% to 5-25% which makes it the best fit to this build.

Phantom Dancer now gives 5% overall movement speed and 75 bonus speed toward enemies instead of 12% which makes it even a better fit to this build since you have no boots.

Death's Dance is now gives 75 Ad instead of 65 and 15% healing instead of 12%. (Always get it ;))

Statikk Shiv bonus damage to minions increased from 75% to 120% (better farming!)

14/06/2016: Updating several parts of the build according to lastest patch 6.11
Overall master yi is not as strong as before with new items and masteries. He also got several Nerf during last patches.
31/08/2016: Updating math calculations for output damage.
10/12/2016: After a few patch all I can say is that there is nothing much changed regarding Yi or the items he utilize (well except some animations and bug fixes stuff!). So the guide is still viable. Good luck!
15/02/2017: passive has been promoted by not wasting the double strike on dead enemies with first strike. Meditate is also buff in my opinion by storing double strike stacks. The build hasn't been changed.
30/09/2017: Updated some minor parts of the build.