Ziggs has some mighty range to push lanes back hardcore. I feel this build keeps him well stocked with firepower and constant damage output. I've found most build do not maximize cooldown reduction and therefore have no chance at fending off an AD ranged carry and run out of mana constantly having to return for mana or conserve your mana. I prefer and endless swarm of bomb tossing chaos. Can't get enough of this champ...

More magic pen, ability power, and some minor defenses just in case. I like to plan for the long haul not just the start, which is why I use the runes that grow as I level when I can. You really shouldn't get hit too often with his range so if you want to swap out the armor runes for something more offensive you may. I would suggest mana regen honestly to ensure you can fire off infinitely.

Gotta love the % bonus to AP in the offensive tree as well as 10% spell pen and more overall damage. Specially since you rarely are hit. I like extending the jungle buffs for when you do get blue buff or red buff early on. Do not overlook ziggs' basic attack damage. I'll talk about that later.

These items max his cooldown and net him some nice autoattack damage as well. Remember with lich bane and your passive your next hit after tossing a bomb could do some major damage.

I start off with the pendant to earn some extra mana regen at the start.

The cooldown boots are nice to get an early cooldown boost to be tossing bombs off as fast as possible at champions as they cross their minions or to chase them back out of exp range and keep them behind their tower.

Rabadon's is an obvious AP choice...

I like the gunblade better than the will of the ancients because it adds some damage to your basic attacks and gives you an extra damaging slow ability for those escapes and or used to ensure a kill doesn't escape your bombs. And you get lifesteal from your autoattacks as well as spell vamp for your spells. It's win for you, but not as much of a team helper. If you have a lot of casters maybe then you should consider stacking will of the ancients together.

Nashor's Tooth is amazing for ziggs, faster autoattacking, major cooldown bonus, nice mana regen, and a pretty nice boost to AP. Cannot fail here.

Lich Bane is a must, every time your passive is at the 4 second mark, shoot off a bomb and autoattack and you'll hit like TNT with your next basic attack for more damage than your spells usually do. And with your low cooldown your passive will be highly effective.

I put the void staff in just in case they have magic resistance. If no one is stacking MR, get something that ups your AP more or gives you a good utility, like another Rabadon's Deathcap or maybe Zhonya's Hourglass. Or if you are having major mana troubles with clarity even, then maybe an Archangel's Staff. I am not a fan of getting this item late though, but if you feel from previous games that mana is still an issue for you then get this early on perhaps.

Bouncing Bomb is the first skill you want to max. It is a vast amount of damage, specifically if you max it early on. 3 or 4 bombs cripple an opposing champ really well early on and keep them very frustrated if you get good at placing them. Just be careful of the jungle since you are extended pretty well by doing this.

Satchel Charge, I usually lead myself with it when I'm running for an escape by putting it in the bushes and when they are about to enter I blast them sending them back a bit off my trail and if they were really close sending me ahead some too. This is also a good spell for team fights since it has a fair radius.

Minefield is amazing for team fights and saving your hide. Make sure to use your bouncing bomb while they are slowed. You can use minefield to keep them from escaping by placing it behind them when your jungle shows up. And a satchel charge to the side of your minefield the enemy champ is closest to can make an anemy champ land in your minefield. Awesome damage and great utility.

Mega Inferno Bomb is wow, if there is a team fight breaking out and you can land the center of it on the enemy champs, your teammates will love you every time. The ability can be launched quite a ways away to save towers for your teammates when they are being overrun in a lane as well. A well timed stun by a teammate in tower range and an insta-clearing of a minion wave could add some nice tower damage to the stunned enemy champion. Maybe even turn it all into a possible kill if your teammate is able to manage it.

Ignite prevents the heals and adds that extra damage you sometimes need. And you get some AP and AD while on cooldown.

Clarity keeps you in your lane, I know most champs would rather have flash or ghost. I just feel that you can safely lane without taking too much damage. You do not need to get those kills every time. Usually making them leave lane to heal will make your growth that much stronger and ensure a team victory. Constant laning is the most important in my book. Rely on your jungle/teammates to come give you assists to ensure you never give a kill to the enemy champions. Better safe than sorry...

Pros w/This Build:
Everything he has does area damage
His passive makes him actually do some good basic attack damage
Major range with his abilities
Has great mana income
Has great cooldown timers
Steals enough hp to stay in lane quite a while
Good income with his area abilities
His passive gives a nice damage bonus as your AP grows

Cons:
Very squishy, not much hp in this build
Can easily be ambushed by champs like shaco/fiddlesticks but not limited to (stay with teammates that can help you escape or peel them off you)
Not the fastest moving champ