After playing with Ziggs for a while, a few nice builds are coming out, and I'm adding mine to those already here. First, a little about Ziggs:

Ziggs is a ranged mage, so he is all ability power. Almost all of his damage comes from his Bouncing bomb, and his Inferno bomb. His passive, which is fairly akin to Shen's, is mostly for cs. Every few seconds, Ziggs' next basic attack does more damage, and each time Ziggs uses an ability, the cooldown is reduced by 2 seconds. Ziggs is very useful in team fights with his range and cc. Overall, if played right, he is extremely deadly.

Pros:
Amazing range on his Q (bouncing bomb) and on his ult.

Good farming and cc abilities.

Very powerful, especially early and late game.

Cons:
Veeeery squishy. With almost all good builds that will come out for Ziggs, none will be other than squishy.

All of his abilities are skill shots. This means that in order to be effective, you must be good will aiming.

Basic attack speed is very low. This means that in team fights, abilities are key.

You can read the skill sequence above, so I won't type it all out, but I will explain it.

First take bouncing bomb. This is Ziggs' main source of damage, and has a much longer range than any character's basic attack. It will do damage to minions as well as champions. Max this skill at level nine.

At second level, take hexplosive minefield. This is a cc ability that will help you kill champions early on. Each mine will slow the enemy champion and do damage, so throw it behind them as they try to run away, or use it to slow them down while they're chasing you.

At third level take another in bouncing bomb. At this level it is fairly simple to charge in and kill your opponent when laning 1v1 in mid.

Take satchel charge at level four. This is another mostly utility skill that is used primarily for escaping seeing as you can bounce yourself with it without taking damage.

Obviously take your ult when you can, and levels 6, 11, and 16. And max first bouncing bomb, then hexplosive minefield, and finally satchel charge.

Now, Ziggs is entirely AP (Ability Power) based. He is all skills, and in the end you want to have as much AP as possible. This would normally be achieved by buying 6 Rabadon's Deathcaps, which would give you +840 AP, but of course we want boots and some other perks.

So, first take doran's ring, which is fairly standard. This gives a little bit of health and AP to start. Buy boots of speed next, that way you get a little up on your opponents, but instead of going straight for sorcerer's shoes, fast build rod of ages. You want to get this asap, because it's passive acts over time. After building the rod, go ahead and get the sorcerer's shoes.

After that, the next four items are really in whatever order you choose. They all give a ton of AP and three give some perks. Getting the ring or hourglass next is generally preferable. Ziggs has about a 2-4 second cooldown on his bouncing bomb, depending on your level, and putting yourself into stasis while your abilities are on cooldown can help win a team fight.

You may want to choose a different sixth item then the deathcap, seeing as it's just for overkill, but I really like being able to knock out half of a tank's health at level 18.

I choose flash and ghost when I play Ziggs. He is slower than most champions, and because he is so squishy, getting ganked is extremely easy. Being able to escape makes all the difference, especially early game. Late game, usually I end up using them to chatch up to prey or gank over walls, etc.

Spells I tried and did not deem effective:

Ignite: This spell is useful for champions who have trouble catching opponents and need to do just a little damage after they get out of range. Ziggs' ult has such a huge range, this spell becomes moot.

Exhaust: Slowing down your opponents so that you and your teammates and do some more damage is all well and good, but Ziggs has a slow as an ability, and again, with his immense range, your opponents can't escape anyway.

Honestly, Ziggs is new, so not everything has been figured out yet. If you have tweaks or suggestions, comment and I'll see about tweaking the build. Thanks!