To many trolls Down voting on Ziggs. So i'll leave this at. Try it, It works great.
Ziggs is not op. People who say that are just bad. Hes only OP when in the hands of someone who knows how to use him :) Ziggs requires all skill shots and timing. So if you cant aim, find a new champ to play.
Ziggs is actually a fun Character to play, and is also a vary powerful mid game to late game character. However a ziggs can not win you the game. He requires a team to back him up. Sec someone gets on top of you its bad news.
Ziggs is a extremely highly targeted character. Do to his range people want you dead.
I started playing Ziggs from the day he was released. All I pretty much play are Ap carries so i thought id give him a try. I haven't been able to have Insanely high killing games with him like other ap Carries, but its cause his high cooldowns make him a great team assister. Not saying you wont get alot of kills. It's all about timing.
I'm gonna try to keep this short and to the point. Most people don't care to read a story to find out what works. Sure it's nice to have a nice looking page, But it don't mean you want to take a hour reading it.
The great and rare thing about this build, It works exactly the same item wise for Dominion.
Thanks for all Troll votes to those people just trying to make their fail ziggs builds. God i love noobs.
Heres at least one picture:Would been a lot better but we won at only 21 mins.Had to add this one. This was just domination
I have lots more just not gonna overwhelm this with pictures.

I go with Magic pen/ armor runes. Mainly cause Im to cheap to buy more ap runes. lol.
But this works good cause of his lack of defense.
If you want, you can also go with Straight ap runes and magic pen. He has a good Ap conversion so it will work out either way.
If your willing to take a hit on magic pen or armor. Movement speed Runes might not be a bad choice also. ~~~

I go with the 9/0/21 in Normal/ranked games.
In dominion i go 9/21/0 for max cooldown reduction.
Reason i go 9/0/21 is for buff increase, xp gained, and spell vamp. You will need the blue buff if you wish to use Ziggs effective. So you want to make sure you have it as long as possible.
In Dominion i go with the 9/21/0 max cooldowns and the spell vamp,xp and buff increase arnt as useful.~~

Archangels- With ziggs low cooldown on his Q you will be spamming skills left and right. This will help with the mp, also will increase your damage by a pretty good amount.

Rod of Ages- This is by far best item for Ziggs, You need to get it early on so you can get the full use of it later on. This is me saying alot cause I NEVER use rod of ages on my Ap carries. This is such a dominate item.

Ionian Boots or Magic pen boots- I go with cooldown boots do to his E and W haven such big cooldowns. they take 5 secs off a level 1 W. And they also help with your spammablity. If you dont feel like cooldown boots are for you. Magic penetration boots are still a great option.

Deathcap- The way that ziggs skills work out on cooldowns this is really were your damage it gonna come from. Only down side is it is vary expensive item. You dont want to get it to soon cause you will fall behind. If you feel you cant farm enough money it might be good idea to save this for last.

Will of the Ancients- You wanna get the Hextech first, just so you have a decent amount of spellvamp. After you get that you will wanna skip to Morello's Tome. Build that than come back to Finish will of the ancients. By than your cooldowns and Damage out put, will Make great use of your Spell vamp.

Morello's Tome- Gives great cooldown and mp regan. Ziggs has alot of issue with his mp sense you spam your Q every 3 secs. And its nice having lower cooldowns on your E and W and especially your ult.

Elixir of Brilliance- Getting this couple times a match before you get Morello's really helps alot.

Meja's - However I have not used it yet. Death cap makes altering this build difficult. If you can afford it do so. Easy to rack up assist on him.
You should also buy hp pot here and there and keep mp pots on tap till you have no room for them. By wards to keep yourself from getting ganged.
Lich- is a great item also If you can afford that as your last item do so.
DO NOT BUY RYLAIS. I gave it so many tries, its so useless for ziggs. Idk why they put it in recommended. Anyone I know that has played ziggs has thought the same thing. That's what your E is for, Not saying it can't be useful. Just not to me.
Update: Forgot to mention that i dont build Archangels in Dominion. I skip it.

Bouncing Bomb(q)- Your main skill, you will use this skill 100x more than anything else you cast. Master this 1st.

Satchel Charge(w)- This skill is near useless. Use it to jump walls. This skills cooldown is horrible, does vary little damage. Even gives you a slight stun on yourself when you blow yourself away. 9/10 Times you will be better off just running vs stopping to cast it. Not saying it dont have its uses, But I believe this skill is broken and needs some fixing. Please let me know if you have any tips to make it better. I've tried everything I can think of with it. And I got nothing.Master This last.

Hexplosive Minefield(e)- Your other main Damage output. This skill is great for trapping Enemies into the area of fighting. However, unless the enemy is a idiot chance of you doing decent damage with it is vary little. You will find blocking/slowing with it is more useful than Using it to damage. Late game its great, Early game it's ok. Master This 2nd.

Mega Inferno Bomb(ult,R)- Great Skill for damage. Has amazing range and damage. However, This skill takes a lot of skill to aim. Has a really high cooldown. Damage on it early game doesn't seem to scale vary well like late game. Great to unleash in middle of a team fight, really can turn the tables on a fight when you hit a lot of people. Master this 3rd.

Heal- I love heal, Great for baiting, saving team mates, saving yourself, Did i mention baiting?

Ghost- Great for getting to your teammates, or running away

Flash- If needed its good for getting away, However if your playing right. You shouldn't be in range of the enemy to make use of this.

Ignite :S - Same as Flash, you shouldn't be in range to cast this normally. So not as useful. However if you feel you cant aim your ult or your Q on someone running away, than this is for you.

Pro's
Amazing Harasser
High damage
Huge range
Low cooldown on his bouncing bomb
Long range ult
Ability to jump walls
Can stop/trap enemies
Aoe Ult
Great mid/late game character
Mid game he can rip apart the jungle
(can jungle cause of his E, However i would not recommend it, Struggles at it cause of mp)

Con's
Highly targeted
Runs out of mp Easily
Struggles early game keeping up
You really have to have blue buff to keep up with your harassing.
Do to only having practically 1 skill, it is hard to execute or get the last blow on kills.
His W is near useless, Sense you have a high cooldown on it. You try to be careful when you choose to use it. It can be good to blow people away from your teammates though.

Simple stay behind your team throw bombs throw your E in front of you or behind enemies.
Front of you to help keep people from getting to you.
Behind them to keep them from getting away.
use Your ult when 3+ people are standing together. HUGE table turner.
Try to make sure you throw attacks from bush's. This will prevent The enemy from knowing your bombs are coming.

Early game try to reserve mp and last hit mobs as much as possible. If Your enemy keeps walking on top of mobs in a group its worth throwing your bomb on all them. Unless your about to get ganged. Try to prevent casting anything but your Q till you have Goddess stone. Once you have The goddess stone You need to get blue. than start firing skills away. Take the jungles Ghost when hes no were near them. They will more than likely spawn again before he gets to them.

Early game you need to focus on farming as much as possible. Mid game you will find yourself running around killing people more than farming. However mid game you will be able to whipe herds of mobs out fast.

All and all Ziggs is a dominate mid/late gamer choice.
If you can be patient early on you will see great benefits from him.
He can destroy other carrys with out much effort. However you have to hardcore kite tanks, If a tank manages to get on top of you.....You more than likely will not get away alive. He does not do well when people are on top of him.
Plan on using your Q non stop.
Don't rely on Your W in middle of field
Use your E as often as possible.
Pay attention to magic def if someone has over a 100 magic def it will make ziggs feel really weak.
Any questions ask me or tell me and ill add them to this. Sorry for any grammar/spelling.~~