Hello, this is my build to Morgana: The Fallen Angel.
This is also my first guide - so be gentle at judging me, come with advice.
I am playing in the 1580's ELO at the moment and I am still rising with Morgana. The update simply made her so damn viable as a glass cannon.
With her high AP ratios and amazing utility I'd say she is a VERY underrated character - if not OP.
A snare, shield and AoE stun and slow! Holy ****, isn't that just amazing? - if you disagree, please tell me why!
I tend to go mid- or top-lane with Morgana since i play her as an AP carry.
Now remember this is just how I like to play her, you can choose to do whatever you want.
This guide will not make you a great Morgana, but it will hopefully help you on your quest to become a master of Morgana.
I hope you'll enjoy reading and later playing Morgana: The Fallen Angel!

The answer to that is: **** yeah she did, before she was an OK character, now she is, in my opinion, top tier!
Here's the notes from the official LoL website:
Morgana

Updated Morgana's autoattack to feel more responsive and increased its missile speed
Base movement speed increased to 310 from 300
Dark Binding cooldown reduced to 11 seconds from 12 seconds.
Tormented Shadow mana cost reduced to 70/85/100/115/130 from 70/90/110/130/150
Soul Shackles
Stun duration adjusted to 1.5 at all ranks from 1/1.5/2
Cooldown reduced to 120/110/100 seconds from 120 seconds at all ranks
Shackle activation time reduced to 3 seconds from 4 seconds
Read that yourself.
So the auto attack thing made her early farming so much better - it sucked before when not using spells.
The base movement speed increase is also great when channeling your ultimate.
Her q, Dark Binding got a lovely buff, it was really needed since the CD was really high on it.
The reduced mana cost on Tormented Shadow is also great, easier time laning and farming!
Now, her ultimate got a nice adjust and buff;
The CD got reduced which is very handy. The stun duration on her Soul Shackles after activation is really nice in the early game and a slight nerf to her lategame. But whatever, 1,5 sec stun is really powerful too. And 1 second at lvl 6 isn't really a whole lot.
Now to the most notable change; the activation time itself on her Soul Shackles got reduced by a whole second. This change allows my build to be viable since all the survivability you will need is Zhonya's Hourglass! Just wait a second then activate it :D (only do so if it's needed, obviously).

Here's some things I like and dislike about Morgana:
Pros:
Strong laner in any lane.
Lovely sustain.
Slow (AoE), stun (AoE) and snare as CC.
High AP ratios.
Almost ungankable.
Cons:
Rather squishy without Black Shield.
High CD's.
Has a skillshot.
Short attack-range (considering that she is a ranged champion).
Has to go in the middle of a teamfight to be effective.

For the marks I use Greater Mark of Magic Penetration. These are simply the best marks for casters, just don't question them.
Greater Seal of Scaling Mana Regeneration I love these seals on pretty much any caster, they will help a lot with the laning.
Another good choice may be Greater Seal of Vitality if you feel like you do not need the extra mana regen. Though I do not recommend them, since Morgana's main farming skill Tormented Shadow costs fairly much mana - so you need the regen to stay in lane with the passive Soul Siphon.
For the Glyphs I go with the Greater Glyph of Scaling Ability Power because I play Morgana as a caster and these will give you the greater benefit throughout the most of the game.
Another good choice could be Greater Glyph of Ability Power if you prefer the early game boost.
Yet again, I do not recommend them a lot since Morgana's farming with skills start at lvl 3.
Now, finally, my favorite quints; Greater Quintessence of Ability Power.
These are simply amazing, +15 AP at lvl 1? Yes please!
Why not Greater Quintessence of Health? - Well, honestly since I tend to solo mid or top I don't feel like these are really powerful. It's 88 hp you get. Might as well take Greater Quintessence of Vigor since they will give you the superior amount of hp over time.
Though nor should you get them! You have your amazing passive Soul Siphon! :D
In conclusion, my choice of runes will help you throughout the whole game and keep you strong in lane and in teamfights.

For masteries i go 9/0/21 standard - remember to pick up improved summoner spells and Utility Mastery .
You should be close to always be carrying the blue buff as Morgana due to the fact that she suffers from rather high cooldowns and a little mana starvation.
Otherwise this is without anything special, feel free to try different stuff like 9/21/0.
Though I personally feel like the best masteries are 9/0/21 since the 21 points in Utility just gives you all you need.
Do I really need to explain more? (If so - just ask me for God's sake!)

I choose Flash and Ignite. Why? - Because Flash allows Morgana to escape/initiate ganks/teamfights/lane fights like no other summoner spell. It is just simply superior in every way in contradiction to let's say Ghost.
Now to the choice of Ignite.
Ignite is a very strong spell for most casters since it just adds to your insane burst combo.
Many times enemies will get away with very little hp and this spell ensures a kill for the most part.
Tip: how I use ignite in lane: I Flash -> Soul Shackles -> Dark Binding -> Tormented Shadow and Ignite. This combo is your most used combo in lane as you do NOT want to miss your Dark Binding
Usually when I use this combo in the lane I can kill my opponent when he/she is at 3/4 hp.
Onto the last of the Summoner Spells available:
Clairvoyance The real support should take this - but if you want to ... go ahead.
Cleanse Nah, not really needed - you have your Black Shield.
Clarity This spell is great for the lanephase but is useless later in the game. I hate it.
Heal Again useful early game but sucks balls later. Don't take it unless you want to, I'm not going to stop you.
Ghost Honestly Flash is just better overall for Morgana.
Exhaust Leave this for the AD's, besides you already have an AoE slow and stun + a single-target snare.
Smite If you thought about taking this for Morgana, excuse me I have to go laugh my *** off. Just don't (unless you're jungling).
Fortify Seriously who picks this? I haven't seen this picked in a long time, but if people picks it usually where you play. Let the tank have it.
Rally Don't take it. Don't. Don't. Don't.
Teleport Having a hard time laning or just want more teleporting mobility? Go ahead take it, seen some other guides recommend it and I cannot say that it's bad.
Revive This is the most underrated OP summoner spell ever! Okay I'm just lying now... This one is for the trolls if you're one, stop being a troll. Right now. NOW I SAID!

I simply max Tormented Shadow first because this will be your main farming- and healing skill.
I normally go for maxing Dark Binding second with a point in Black Shield in lvl 4.
Of course I'll grab my ultimate whenever available.
I want to say that this skill order is not strict; though I always max Tormented Shadow first, but sometimes i go for a single or two points in Black Shield.
You have to be versatile in skill order aswell as items.

My build for a glass cannon Morgana is as following: Boots and 3 Health Potions. Moving onto two Doran's Ring (sometimes if you're having the time of your life/need extra survivability go for 3 Doran's). Following I upgrade my boots to Sorcerer's Shoes.
Then I rush a Rabadon's Deathcap for some insane AP. Now you need some survivability and the perfect item for you in this case is Zhonya's Hourglass! It provides some nice armor, AP and the best of all; the active state which leaves you invulnerable for 2 seconds.
Now the active state works well with your Ultimate as the activation time is not broken when activating the state.
Finally if the game continues grab a Void Staff for the AP and penetration.
Now I haven't actually tried a game that would last longer than these items, but if you get it I'd recommend a Guardian Angel as reviving from it WON'T break the active part of your ultimate - Soul Shackles.

Some may want to troll me and say: DUDE WHERE IS YOUR Rod of Ages?? - To that I say: Ok, you're right, RoA is a great item for Morgana, but I feel like this item should only be grabbed when you lack very early survivability.
Feel free to grab it anyway, but I skip it because Morgana scales so damn well off of AP and I don't need the early survivability from it - besides it'll make your mid game dmg lackluster compared to my usual build.
After Morgana's buffs all the survivability you will need in mid- early lategame is Zhonya's Hourglass's active state.
The last thing I want to say about my items is my boots - Sorcerer's Shoes. These are super awesome for Morgana, some may ask: Why not Mercury's Treads? - Because your worry isn't how long nor whether or not you get CC'ed. There is no kind of CC that can stop your ultimate completely. So my worry isn't how long the CC will last.
Though I dont say that Mercury's Treads is a bad item :) (Of course I'll grab them if they have insane amounts of CC, but this is not usual)
Keep in mind that this is just MY PERSONAL OPINION. Feel completely free to change around in something.

I tend to go mid- or toplane with Morgana since as an AP caster you will need the level advantage and Morgana can handle mid with ease due to her passive Soul Siphon and her Black Shield since your enemy at the mid will mainly be a caster.
So why is she also a viable top laner? - Yet again Soul Siphon!!! The Melee tanky AD chars mostly go top lane so what if they jump me like madmen?? - The answer is simple; Say "**** YOU *****" with a Dark Binding go a little away and cast Tormented Shadow on minions to get your hp back up (alternative: cast it on the enemy champion to damage them if you do not need the hp gain from minions).
Your goal in lane is to farm up and not really harass a lot before lvl 5-6 then go in for a kill.
Keep in mind that you may have trouble auto-attacking to harass since Morgana's auto-attack range is horrible.
So skill sequence in short:
Mid: Max Tormented Shadow, get Black Shield in lvl 2, max Dark Binding after W.
Top: Max Tormented Shadow, get Dark Binding in lvl 2 and max it after. Grab a single level in Black Shield at lvl 4.
In both lanes you obviously want to get your ultimate when available.

August 17 2011: Published the guide.
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Even if it's trolling/negative feedback you want to give me. Thanks.