Thats my build for Cassiopeia.She is one of my mains , I play her as a viable AP carry , a little survival and tons of damage if unchecked and left alone.I hope you enjoy it :)

Updates

05-05-2011
1-Added icons for spells , runes and items.[Thanks MrSickolufugus!]

2-Added Abyssal Mask and Lich Bane to optional item list.[Thanks MrSickolufugus!]

3-Added Mejai's Soulstealer to item list.

4-Typos corrected.

Pros :
1-Very good AOE damage mixed with a decent single target damage.
2-Very useful ulti in teamfights, can turn tide of battle if used correctly.
3-Very good kiting potential , even matched with Ashe.
4-Great passive.
5-Great Harrasser in laning phase.
6-When ganked , %90 of times she can countergank them with ulti :)
7-Good playing makes enemies RAGE !

Cons :
1-Very squishy, so wrong positioning in teamfights usually leads to death.
2-Usually lading the ultimate in correct way is a pain.
3-Damage is based on DOT spells.
4-Team dependant.Needs a good mix of protection and support.
5-Failing a Noxious Blast + Twin Fang combo %90 of time leads to enemy escape or , even worse , can lead to death.
6-Going reckless on harrassing can make you out of mana frequently.

I prefer Greater Mark of Magic Penetration marks . which are good for every caster.Also i get Greater Glyph of Ability Power and Greater Quintessence of Ability Power, because Cassiopeia benefits greatly from ap at early levels- Noxious Blast gets 0,9 ap ratio, having an AP advantage in early game is devastating.
About seals : I prefer Greater seal of vitality for some defense since Cassio lacks survival and has a low health pool.But you can get anything you prefer/you already have.

My facorite summoner spells for Cassiopeia is Flash + Ghost.Since she has no escaping mechanisms that spells helps her to escape.With Ghost active , when you hit a enemy with Noxious Blast you are faster than all champions in game. Flash is for jumping over the walls is very good :)

Other viable options :

1- Clarity : Cassiopia can go out of mana even with her passive , if your enemies are tough and you are not skilled enough to noxious blasts for harrassing you can go out of mana very fast.Get this if you feel like lacking mana in early game.That spell loses its usefulness in late game and after getting Tear of Goddess.

2- Clairvoyance : This spell is good for map controlling , exploiting ganks and keeping track of enemy junglers.

3- Ignite : Adds another damage over time spell in your collection.I dont prefer this a lot but its good aganist self healing champs like Vladimir, Irelia or Dr.Mundo.

4- Teleport : Good for ganking but not good enough for Cassiopeia.Let your pushers get this spell.

Spells you should NOT get :

1- Fortify : Let your Tanks get this spell.

2- Exhaust : You should not going to need this , you should not let someone to get in your range.

3- Heal : Maybe a life saver sometimes but you can survive better with flash or ghost.

4- Cleanse : Cassiopeia is very fragile, even cleanse cant save you if you were in a wrong position.

5- Revive : You are not going to need this.

I prefer to max Noxious Blast first , deals pretty decent damage in early game, also good for harrassing in lane.Then I level Twin Fang as secondary skill , leaving a point to Miasma at level 4. Miasma is needed for Ulti + Q + W + E + Q combo , while enemies are stunned with Petrifiying Gaze , Miasma + Noxious Blast + a few Twin Fangs are usually kill a squishy or make a bruiser run away.Finish them with Noxious Blast :)

I start off with a Meki Pendant + 2 health pots.Both are good for laning phase , having meki pendant allow you to harras easily without going out of mana , health potions gives a bit survival on lane.After i upgrade my Meki Pendant to Tear of the Goddess , to make sure ill never go our of mana in fights- spamming Twin Fang is a real mana hog also ulti costs a decent amount of mana early levels.
Now you are going to ask : Why there are only basic boots in item build section ? Easy.
There are some viable options for Cass , you should get which one you need in game.
Viable options are these:
1- Sorcerer's Shoes : Basic boots for every caster.You notice a significant damage boots when you get these.But these boots does not provide any survival stats.I only recommend these if you know what you are doing.Pick only if you have a decent support/tank guarding you or you are not getting focused/ganked a lot.
2- Mercury's Treads: These boots gives a nice amount of Mres with a plus of CC reduction , which is a huge plus.But these are not recommended if enemy team doesnt have a lot of CC's (doesnt happen much).Great survival but lowers your damage output a lot.
3- Boots of Swiftness : Ultimate boots of kiting.If enemy has champs which are needs to be kited : Thats what you are looking for.With MS boost from Noxious Blast + slow from Miasma + Rylai's with these boots makes sure of you never will be catched ! But still these boots reduce your damage output.

After getting boots and Tear of the Goddess, go rush for Hextech Revolver ! That item provides great survival since Twin Fang DOES benefit from spellvamp,which you are spamming in fights ,that item will give you decent amounts of life regen.You can solo dragon with that item easily :) Also helps you to survive harrassments easily.
After getting revolver , you should be able to solo most of champs in game.You should be getting some kills/asists with that items easily.

Next item : Rylai's Crystal Scepter. This.Is.Best.Item.For.Her. in game.Provides decent amount of HP , nice amount of AP and slowing spells ! Throwing a Miasma to an enemy's escape path will severely cripple him , also you will have a spammable slowing attack with Twin Fang and you will find slow useful while running away / kiting enemy champs with Noxious Blast.

Rabadon's Deathcap : Do i have to explain why we get this ?

Archangel's Staff : You should upgrade this as last item , when you have max stack of Tear of the Goddess.

So you should be asking now : Why there are only 5 items there ?
Answer is : Last item you are going to buy depends how game is going.
Viable options are :
1- Zhonya's Hourglass : That item is very effective aganist heavy AD teams , also shines at late game.Decent AP + good armor makes this item really good.Also has a nice active.

2- Banshee's Veil : An enemy AP doing well ? Get this ! That will lower enemy's damage output and literally annoying if he/she is a playing combo based champ.You dont have to wait till end of game to get this item , you may get an early negatron cloak before buying deathcap.You can also decide completing this item before deathcap : Dealing low damage is far better than getting nuked down and dealing no damage at all.

3- Abyssal Mask : A very good item has good AP mixed with decent amount of magic resist.Also you will find magic resist reduce aura very useful if you dont have Sorcerer's Shoes.

4- Lich Bane : An interesting item for Cassiopeia.Gives good amount of AP , a little amount of Mres , %8 movement speed boost.Also beacuse of you are spamming Twin Fang a lot , you will get plenty of procs.I just noticed Cassiopeia DOES autoattack between casts of Twin Fang so procs are not wasted if fight is stationary.

I prefer these items but you can sacrifice any of item in the list to buy more defense if you wish.

About Mejai's Soulstealer : This item is good if only you are doing very well and not getting focused down.If you lack AP in early game and enemy team is ignoring you (without AP you do normal amount of damage).You can get stacks easily because your 3/4 of spells are AOE , getting asists should be easy for you.

Farming is not hard with Cass , even at level 1 you can get ranged minions with 2x Noxious Blasts.But the real threat is over pushing the lane and leaving you vulnerable to ganks.I'd recommend to buy wards to protect yourself and push freely.Getting a few kills with a good CS is enough for her.Also get the blue buff everytime you can.

Early Game

In early game she is a boss in the game.Dont hestitate to use Noxious Blast to nerve your enemies ! With great harrassing potential and able to punish mistakes so hard you should be able to dominate your lane easily.That means you should be prepared for ganks.I'd recommend buying 2-3 wards whenever you go base.

Mid Game

In mid game you should have your Tear of the Goddess , your boots and your Hextech Revolver.You should also have some core items for Rylai's Crystal Scepter or maybe even you have it too (depends on farming).You are a real threat in teamfights if unchecked and left alone , which usually happens -opponents usually think there are more dangerous(!) assasins or carries in team , you should devastate enemy team with a well used ulti and spamming Twin Fang to targets which needs to be focused.

Late Game

In late game , positioning is everything for Cassiopeia.Enemy team will realise you are a REAL threat , they will try to shut you off in every teamfight.You can counter that attempts with your ulti , if they bring fight to you you can disable all enemies with a single skill.Also dropping a Noxious Blast + Miasma on them will cripple them , you can leave the place safely.Then let your team to do rest if you are dead.

Cassiopeia is very fun to play , she is a great damage dealer but since her spells are based on DOT's you need to survive a few secs to win a fight.Also she is very very hard to play and master , if done well she is a real threat in game.Good positioning and good usage of ultimate leads to victory , bad positioning and poor usage of ultimate leads to defeat.
My Tips for Cassiopeia :
1-Using Twin Fang on stationary targets and enemies stunned with Petrifying Gaze causes them to take a lot of damage.

2-Hitting with Noxious Blast is easier in early game, when most of champioms movement speeds are still low without any boots.

3-Try to lead enemies path to hit Noxious Blast to ensure you are going to hit them.

4-Have nerves of steel , delaying Noxious Blast to guarantee the hit is far better than random spamming of it.Try to throw a Miasma to slow enemies down and guarantee the hit.

5-Hitting same enemy with Noxious Blast several times usually decreases morale of that player , you can use this advantage to deny him in lane.But be careful : That will increase you chance to be ganked :)

6-Dont hestitate to use your ulti when you face 3 or more enemies initiating a teamfight , that usually means a win even before the fight starts.You can also wait assasins and other squishies to initiate teamfight to use ulti.For example if enemy has Kassadin , Tyrndamere and Katarina , its wise to delay ultimate and use it after they are engaged.

7-Cassiopeia's Petrifying Gaze synergises with most of champions in game.Having champs like Malphite , Nunu , Shen , Sona , Amumu in your team usually leads to victory.

8- Noxious Blast can be used to scout bushes , you will see a movement speed increase buff if you hit an enemy champion.Throw Miasma to force enemies run out of bushes.

Thats all i can say :)
Thanks for reading my build.
Please comment while you are voting.