Hello and welcome to my build. This is my first build, so please don't say it's terrible. I'm still learning. Any constructive criticism is accepted. If you would like to contact me i have skype/teamspeak/ventrilo/email/in-game. Please try this build out before you rate it.

For runes i like to go for armor penetrations for my marks and quintessences for the extra "oomph" when you hit, early to late game. The seals and glyphs i go for critical chance for early crit chance for pushing back or a nice first blood.

For my masteries i like to go for a custom 23-1-6 build. It was originally for my teemo build but i transitioned to Gangplank and it actually worked very well.

I like to grab boots of speed then a hp pot and mana pot to keep me in my lane longer, even though remove scurvy will heal alot early game. Next I try to stay in the lane long enough to get enough gold for the Berserkers Greaves. After this i try building my phantom dancers by getting the zeals first then the cloak of agility and last the dagger, I like to finish both of the phantom dancers at the same time if not seperately. Next I try to build up enough money to just buy the Infinity Edge straight away, but if I'm having a bad game I'll just save up for the B.F. Sword. After getting infinity edge I will stack up the blood thirster by first getting the vampiric scepter, then the B.F. sword. After the Blood Thirster I will get the Hextech Gunblade.
OPTIONAL ITEMS:
Trinity Force (Helps with damage your ulti and even more attack speed and crit chance)
More soon..

For my skills I tend to max out parrrley first because it will be your main damage output early game and a great way to last hit minions as well as get some nice bonus gold. Next I get remove scurvy because this is a great heal with a built in cleanse. (What more could you want?!) After that i get raise morale, this skill is needed greatly for late game teamfights for the upper hand on the enemies. The passive is also really great for moving around even faster and doing more damage. I level up my ulti whenever possible.

For summoner spells I grab Exhaust and Flash, these are my two favorite because exhaust is great all game and gets even better with your mastery. I take flash because this is one of the best, if not THE best escape summoner spell in the game. It's like shacos deceive without invisibility.

Other spells:
Revive: No one needs this. Not even butt pirates.
Teleport: Maybe for 5v5.. but you move so fast you dont really need this at all...
Rally: GTFO
Heal: YOU HAVE ONE!!!!!1!!!1one11!!
Clarity: You won't be needing this.
Cleanse: Do i even need to tell you? Really?
Fortify: Leave this to the tank(s).
Smite: You won't be jungling.
Ghost: Maybe if you want.
Clairvoyance: If no one else on the team has this.
Ignite: Only useful for first blood or against mundo or vlad.

With this build I either carry the team or I do very well and support my team with my ulti and other abilities. This build I cannot guarentee a win for you because you actually need some skill to play Gangplank. Gangplank is a glass cannon, so don't expect to 3v1, or 5v1 the entire enemy team and think you can kill them. (unless your overfed, we're talking 40-0 here.) Anyways, Good luck playing with this build and I hope you like it! Don't forget to comment and use the build before you rate!
This build is still under construction so any constructive criticism will be appreciated!:)

Gangplank is a great team player for ranked games. If you're looking to play ranked i wouldn't reccomend using this build, mainly because it requires you to get fed a little bit and in ranked you more or less won't be as agressive as in normal. Gangplank has the only deny in the game and he can cost the enemy team valuable exp as well as gold.

Pros:
A huge amount of damage output mid to late game depending on how your game is going.
He can either carry and/or support the team alot.
His ulti is like sex, it's very pleasuring when you get kills and it sucks when it's over.
His heal has a built in cleanse. Nuff said.
Raise morale not only has a passive, but nearby allies get the buff too.

Cons:
Gangplank is a glass cannon, he does ALOT of damage but dies extremely quickly.
If you are owning the other team completely then you are most likely going to be targeted first.
If you miss with your ulti, your probably going to be ridiculed, but it's fine just make sure you get them next time.