One of the Champions who I had the most positive experience playing was Gangplank, and here I am sharing this experience with you also to receive feedback. That is my First Guide and is mainly to discuss in comments! So before downvote, lets talk!
But let's go for what interests.

"Everyone" says that Gangplank has problems with Mana in early game, but if you want make difference in mid and late game you should not save Mana! I tried solve that with Mana Potion, Crystalline Flask including Health Potion to save Remove Scurvy but it is not enough!

I often saw people solving this by recalling. I consider it extremely wrong. just as in chess, back piece is a play lost. I say this because displacement is extremely expensive.

Parrrley can infringe considerable damage, therefore a great harass skill. Can also be a great farm tool with bonus gold. but and your Mana? Yarr!! Let's solve that problem with Tear of the Goddess!

With these strategies you can pass through the storms of any powerful Carry Enemy and guide your crew to victory!

Pros

Cons

+ Bonus gold with Parrrley + Good harass with Parrrley + Can farm behind minions with Parrrley + Health regen with Remove Scurvy + Remove Crowd control with Remove Scurvy + Help your team anywhere with Cannon Barrage

- Mana cost of Parrrley - Mana cost of Remove Scurvy - Without ability to cross over walls - Need good strategies to make difference

Grog Soaked Blade: Passive Gangplank's basic attacks apply a poison debuff for 3 seconds that can stack up to 3 times. Each stack deals 3 + (1 x level) magic damage per second and slows the target by 7%.

That is your Crowd control. Ok, that's not a Powerful Crowd control, but you can use so much easly (your basic attacks and Parrrley apply it) wounding the most vulnerable enemy to ensure a kill or take the control of the team fight.

Q:

Parrrley: Range: 625. Cooldown: 5. Cost: 50 / 55 / 60 / 65 / 70 Mana Gangplank shoots an enemy with his pistol, dealing 20 / 45 / 70 / 95 / 120 (+1.0 per attack damage) physical damage. Gangplank refunds half the mana used and gains 4 / 5 / 6 / 7 / 8 extra gold if Parrrley deals a killing blow. This ability can critically strike and applies on-hit effects, including his passive.

With a good range to a melee Champion, with that ability you will farm well and be rich! But coupled with your passive above, you can harass or chase easly too.

W:

Remove Scurvy: Cooldown: 22 / 21 / 20 / 19 / 18. Cost: 65 Mana Gangplank consumes a large quantity of citrus fruit which removes any crowd control effects on him and heals him for 80 / 150 / 220 / 290 / 360 (+100% of ability power).

Undoubtedly a heal that also remove any Crowd control is over power. Be careful with the cooldown, the safest thing is keep to the enemy Crowd control in early game.

E:

Raise Morale: Range: 600. Cooldown: 20. Cost: 50 / 55 / 60 / 65 / 70 Mana (Passive): Permanently increases Gangplank's attack damage by 8 / 10 / 12 / 14 / 16 and his movement speed by 3 / 4 / 5 / 6 / 7 %. (Active): Gangplank fires into the air, disabling his passive boost but inspiring himself to gain an additional 12 / 19 / 26 / 33 / 40 attack damage and 8 / 11 / 14 / 17 / 20 % movement speed, with nearby allied champions receiving half that amount for 7 seconds. He regains the passive when the buff ends.

This one part of your combo, activate it before use Parrrley (especially when you have Sheen). It help much your team, don't forget to use it to run, chase, destroy turrets, etc.

R:

Cannon Barrage: Range: Global. Cooldown: 120 / 115 / 110. Cost: 100 Mana Gangplank signals his ship to fire 25 cannonballs upon target area for 7 seconds. Each cannonball deals 75 / 120 / 165 (+20% of ability power) magic damage to all enemies hit. Enemies caught in the area of this ability are slowed by 25% for .25 seconds, with the duration refreshing if one stays in the area.

Here we have another Crowd control but to be used globally. Of course you can use against your lane's enemy, but the pressure you can cause in other lanes is much more advantageous, so be prudent.

With the Runes I don't have a concrete opinion. Seal of Armor as always. Mark of Armor Penetration since you are on Top lane and always the enemy has armor. Glyph of Scaling Magic Resist because you will have a few items for Magic Resist. Quintessence of Attack Damage will give you damage to harass.


SUMMONER SPELLS

Flash Essential to escape over walls. Great surprise action.

Teleport You will be able to push your lane, recall to rest/buy and teleport back to lane keeping the pressure against your opponent. In the mid/late game it give mobility to help your team.

Ignite If you dont need teleport, the best choise is that. Ignite will break the heal of target and burn!

Tear of the Goddess Essential to execute the strategy of this guide. Without this item you may find yourself without Mana when with a unpredictable movement of the enemy, you even can use Cannon Barrage to help your team. In the Early Game you can collect gold, harass with Parrrley and get away from dangerous situations with Remove Scurvy.

Sheen Your item of damage. This item has a passive called Spellblade (After using an ability, your next basic attack deals bonus physical damage equal to your base Attack Damage), that work with Parrrley.

Stealth Ward I'm not highlighting just to remember. Put that to push your lane farming safely. And often teleport to the ward is more astonishing than using on minions or turrets.

Mercury's Treads Most of the items are for phisical defense, in doubt use this boot.

Iceborn Gauntlet A good evolution to Sheen. This one give armor, cooldown reduction and upgrade your damage to a circle with slow ( Parrrley is considered melee).

Frozen Heart Much more armor and cooldown reduction. But most important is the special effect that reduces the attack speed of nearby enemies by 20% (1000 range). My personal experience it is essential against strong AD Carries, like Vayne.

Spirit Visage This is a important magic resistance with a upgrade to Remove Scurvy. It is important if your Top opponent causes magical damage, like Kennen.

First of all, remember: this build is to help you follow a specific strategy, you will not be a carry or take much kills; probably your actions will lead to gain the focus of enemies, but what a tank should do? Your mission is open the way to your (both) carries!

Like Nasus need farm with Siphoning Strike to be strong in late-game, you need farm with Parrrley. The difference is that you will have gold to become stronger.

With this in mind, when you arrive your lane, the objective will be farm to take 775 gold, the price of Tear of the Goddess plus a Stealth Ward. Use your first ward in the river to prevent gank and push your lane or keep safe with the turret in your back.

With the Gold, go buy the Tear of the Goddess+ Stealth Ward and back to your lane using Teleport (can you use it on your placed ward and renew with another one).
Now is a new beginning, soon you will have enough Mana to harass and farm.

Now we must begin to study the situation of this game:
Your opponent can not intimidate you? Stomp him with your damage item ( Avarice Blade or Sheen).
Your opponent is giving too much damage? Purchase your defensive items!

You have some tasks in mid game:

• Farm using Parrrley;
• Take care of your team with Teleport or/and Cannon Barrage;
• Disturb your opponent.

One thing that I believe you should do is pay attention to what your team is saying about enemies. They faced the carries, they should have a good opinion about which carry are stronger. Then decide if you need to make magic resist, health or armor.
In worst case the magical damage will be problem, which will force you to complete Spirit Visage and probably Aegis of the Legion if your jungler is not already doing.

Proceeding have three possible situations:

• Probably, in most cases you will be on the defensive, but do not be intimidated. If your opponent destroy your turret, just remember to keep your lane forwarded and feel free to end your "lane phase" to help the others. Our opponent will do the same if you don't keep your lane forwarded.
  
• Hardly you will be getting destroy enemy tower, unless your jungler has helped. In this case do the same, end your "lane phase".
  
• If you are in a stalemate but completed two items, is already too late and monotonous, force everyone to leave the "lane phase" pushing another lane or threatening to do the dragon.

Why the game is not over yet? (really)

You can now sell Tear of the Goddess or upgrade to obtain Muramana (this will giving 38~56 AD passively and 116~170 activated, depending on your items). But Statikk Shiv gives movement speed and critical chance.

The game may be many possible situations but this build prioritizes winning team fights, your final structure allow you to face the enemy carry.
Take care of AD/AP Carry first of all because they will not be able to escape, or choose one that is poorly positioned (never a Tank enemy). That you choose to target will probably be dead because the disengage is hard here.

Try do not fight into the jungle, walls probably will be more hindrance to you than your enemies (but if it is just the strength of your team, the way is to adapt).

Finally a more practical point of view, trying to be as scientific as possible, trying to ignore the ability of those involved. I have to assume that these enemies will do their default build.

obs: I might remove some of these listed, add others or I may decide to group them (tell me what you prefer).

Akali (Coming Soon)

Cho'Gath (Coming Soon)

Darius (Coming Soon)

Fiora (Coming Soon)

Garen (Coming Soon)

Irelia (Coming Soon)

Jarvan IV (Coming Soon)

Jax (Coming Soon)

Jayce (Coming Soon)

Kennen This little plush throws shurikens and causes shock, if you are the target of 3 abilities in less than 6 seconds, you will be stunned (save Remove Scurvy to prevent it). Use the minions to protect against shurikens and prioritize Spirit Visage. After lane phase this one will be a threat to your carrys, so don't allow him to engage a team fight.

Lee Sin (Coming Soon)

Malphite (Coming Soon)

Nasus (Coming Soon)

Pantheon This spartan has a large shield and will block your Parrrley and it works after he use 4 spells, then not spend mana for nothing. Use the minions or your basic attack to remove it. He also has a stunning leap and after this he will cast Heartseeker Strike, so to prevent this combo use Remove Scurvy and walk away. Careful not to waste your Cannon Barrage when you see the target of Grand Skyfall because he can still cancel.

Poppy (Coming Soon)

Renekton (Coming Soon)

Rengar (Coming Soon)

Riven (Coming Soon)

Shen (Coming Soon)

Singed (Coming Soon)

Tryndamere (Coming Soon)

Volibear (Coming Soon)

28/11/2013 - removed mastery Feast.
22/11/2013 - added tricket (preseason 4).
22/11/2013 - removed oracle (preseason 4).
20/11/2013 - new masteries (preseason 4).
30/10/2013 - matchups of Kennen and Pantheon.
29/10/2013 - new chapter, talking about matchups.
29/10/2013 - talk about Philosopher's Stone at introduction.
25/10/2013 - more about items into gameplay.
24/10/2013 - new formatting of Items and proposal.
24/10/2013 - re activate C2V.
23/10/2013 - more details at Gameplay: Beginning.
23/10/2013 - new ToC for the chapters of gameplay.
23/10/2013 - new formatting of Champion Abilities.
22/10/2013 - more explanation of mid and late game.
22/10/2013 - removed from the intro where says I'm Brazilian.
21/10/2013 - better explanation of Grog Soaked Blade potential.