After some time I'm updating this build. The reason I didn't update this was because so many things have been changed and most of them are no longer useful. Essentially killing Alistar
Some things have been truncated with minor changes. The build still follows the same concepts. But now it is considered off-meta

To put it briefly, All the item changes and changes to crit have put you at a handicap. Your powerspike changed from 2 items to 3(excluding Boots)

Here is the Alistar build for this season.

Build:

AD

Play Style:

Off-meta

Old Build:

https://archive.ph/9hi12

CONQUEROR

No more Press the Attack.
Conqueror is good for early game plays.

Hail of Blades

The only use for this is Burst Damage. If all your autos crit it's a guaranteed kill on any squishy.

Triumph

This helps tower with diving, if you are being focused by the tower and are taken to low health, if you get the kill or assist, You can survive the tower's last hit if your ultimate Unbreakable Will is up.

Last Stand

Majority of your fights since you're not tanky you'll be taken to low health, but with your ultimate Unbreakable Will your chance of survival will increases, and at the same time this boosts your damage output

legend: tenacity

optional but not necessary since you have your ultimate.

Presence of mind

No longer useful

coup de grace

Kill low HP Champions

Passive

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• If you are reluctant to recall then your passive can keep you in lane but probably at the cost of farm, and you will
  likely not have mana, if you're low on health. it's best you recall.
• You can save yourself from Ignite if you kill a minion to finish your passive. 7 minions must die near you to activate your passive

Pulverize

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• You can block champs from dashing/jumping on to you if timed correctly.
• You can Use it on minions to stop minion agro.
• You have the best chance to kill enemy champs while they're stunned by your Q.

Headbutt

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• Your main engagement tool.
• Max W first
• You can catch an enemy champion if they flash away if you Headbutt a minion close to them
• You can use it to escape by Headbutt a minion that's close and push someone away from you.
• You'll be vulnerable to ranged attacks if you don't have this ready.
• You can also use it to last hit an enemy champion if they're out of your reach.
• If you're fast enough you can basic attack, place Ignite or use Tiamat on a target at the end of your W(does
  
  not work close range).
• You will miss Pulverize if you Headbutt at basic attack range.

Trample

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• Stun target for extra attack time.
• Can be used to Find invisible teemo.

Unbreakable Will

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• You can remove disables with your ultimate.
• You can trick and enemy to engage you and use your ultimate at low health.
• Makes you tanky while able to do allot of damage.
• Can cost you a fight if used at the wrong time.

Starting Items

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Boots of Speed

For Mobility. One usage would be to Headbutt, Pulverize an enemy and run away. You'll be faster than the enemy.

OTHER START ITEMS

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This is just for the people who would not be able to accept Boots as a starting item.

Long Sword

This doesn't have to be your starting item but it's because the new runes, have adaptive damage. You could start with a Doran's Blade although optional

ESSENTIAL ITEMS

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These are items meant to maximise the use of your abilities and basic attack at the same time.

Berserker's Greaves

• First Item
• Helps you keep up with the target while Trample is stacking

NAVORI QUICKBLADES

• Second Item
• If you crit you will get some cdr on your Abilities
• Helps with Ability Haste

Phantom Dancer/Mortal Reminder

• Third Item(s)
• Gives you attack speed
• Gives you Movement speed above 400. (Requires Boots)

Burst Damage Items

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Essence Reaver

• More Ability Haste
• Only just for Burst Damage

Trinity Force

• Good for extended fights
• Adds more Ability Haste

Maximising Damage

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Unlike Burst Damage Items These do more damage per hit rather than in one hit. But require all essential items.

Infinity Edge

• Increases critical strike Chance and Critical Strike Damage.
• Probably the worst Crit item. If not the worst item overall.
• Adds more than 100 extra damage to your auto attacks that Crit but not usually more than 200 damage.

Titanic Hydra

• Take this instead of Infinity Edge You will likely do more damage overall.

Final Item

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Anything that would give you Ability Haste, Attack Speed or Life Steal.

You can't Snowball hard like the old Alistar With the old items. So you'll probably never get to full build before the game is over

Pros:

Surprise effect.
Shred any carry.
Good CC.
Burst damage
Counter enemy gank.
Guaranteed kill when you Gank a lane.
When you're ahead you can snowball(probably)
Late game monster (with your ult).
Tanky without tank items.

Cons:

Eat's mana for breakfast.
Can't farm so well early game.
You can't win a 1v1 with your ult if you engage incorrectly .
Reliant on team.
If behind then difficult to get back.
You're useless if your Headbutt is wasted. (you will be kited)

Flash

You will always need flash to either flash to kill, or flash to escape etc.

Ignite

Ignite can help you get a kill early game.

Team work is very important early game, When you've pushed the minion wave. Your laner will never expect you to be gone, so take the chance to gank bot or top. And do it as frequently as possible. Until you've got your Items.

Be sure to never die alone, or if you are making allot of mistakes and died multiple times stop and just play safe, because if you fall behind it could cost you the game.

The More CC on your team the better. Which is why this build takes mid lane, and your team comp could have cc top, cc support and cc jungle.

Crit has been Nerfed really hard. It'll be a miracle to win any game through sheer force. You can only win by outplaying.

Please view the video below to see some examples.

Video