Introduction: Morgana is a support character, and anyone who tells you, or plays differently...well, as condon would say, "Is bad and should feel bad." This build can't solo a super minion, can't push lanes and isn't for noobs. Read on if you're still interested.

Runes: Your runes are pretty open, but I currently run:
Red: AP, MPen or Hp.
Yellow: Mana regen/level, but dodge is solid here as well.
Blue: AP or Hp.
Quints: Move Speed, since Morgana's pretty slow, but Hp works here too. Also, 3 gold/10 is something else I've had luck with, since my build is terrible at farming.

With all hp red/blues, it's about 180 at 18, but I don't have the IP for them or the dodge runes, and I played Morgana ALL wrong when I first started out. Quints are another 100sh, but I like move speed, especially early on. You don't need CDR blues, that'll be covered later.

Skill Build:
Q
W
Q
E
Q
R>Q>E>W

Max out your Q first. It's what you use to snare and run, or snare so your carry can get a kill. You don't need money, you need assists, like 100 of them. A good game for Morgana is 0/(anything under 10)/31978478952. Give your carry the kills. Or the tank. Either way, you don't want them.

Masteries: I run a silly 0/16/14 hybrid deal. Again, no CDR, your items will take care of that.
Defense:
1 Resistance, 3 Hardiness
4 Evasion
1 Nimbleness, 3 Harden Skin
4 Veteran's Scars
This gives you solid early game, with a lot of hp to play with at level 1. That should keep you out of trouble until your build gets going.

Utility:
1 Teleport, 1 Ghost, 3 Perseverence
4 Awareness(XP)
3 Meditation
2 Quickness
If you want, you can pick up 2 in the regen and 3 in Quickness. Again, I play around a lot, so do what you want here.

Summoner Spells:
Ghost/Teleport
Black Shield + Ghost will, 90% of the time, get you out of any trouble you're in. Unless they bring out all 5, you shouldn't have a problem getting away, since you can't be CC'd.
Teleport is for getting where you need to be(back to your lane, into the fight, etc.)

Other spells you might enjoy:
Flash: I've never had much luck with this. Ghost lasts longer and with her E, you should be gone before they can get you anyway.
Clarity: It works, and you can fool around with your masteries to get the improved version, but Soul Shroud and yellow runes should keep you up just fine.
Clairvoiyance: I'm never any good at picking where to put it, but as support, it can be really helpful. (But I prefer to drop wards everywhere, read on to learn more!)

Things not to take:
Ignite: You aren't looking to kill anyone.
Exhaust: See above.
Rally: Lols.
Fortify: Yah...
Cleanse: You have black shield. Use it.
Smite: Never been a fan, but if you have trouble farming, it may be worth it(make sure to get improved from Offense if you do.)
Revive: Lols.

Items:
I'm pretty rigid in the items I make, but not the order. I like to finish games with:
Merc Tread's: These will be your boots 99% of the time. If they have very few or no CC, get Tabi.
Aegis: Yay for team buffs.
Soul Shroud: Yay for team buffs and CDR.
Frozen Heart: Yay for other team debuffs, mana and CDR.

Most of my games, I don't get a chance to finish even these, but Aegis is always last. With Shroud and Heart, you have your 40% CDR, lots of mana, lots of mana regen, and decent hp.

Starting:
Mana manipulator.

As you go back, try to finish Soul Shroud first, it's the most inconsistent of the items, since the belt takes 1110 gold, and every part of Frozen Heart can be done in small pieces(The most expensive parts are the Chainmail at 700 and the heart for 800).

Once you get Soul Shroud/Frozen Heart finished up, get your Aegis. Now, most people will say that the earlier you can get Aegis, the better. Well, sorry, you need CDR before anything else. More Black Shields and more Dark Bindings(for running or assists), is more win than the little buff that Aegis gives. Besides, both the Shroud and Heart are bigger buffs/debuffs for your team than Aegis.

After you've finished those 4 items, if the game is still going, the rest of your purchases should be wards. Sight if they have no stealth and vision if they do. Drop them everywhere. Any piece of brush your team goes near, drop one. You can buy 6 wards at a time, and you should fill up every time you go back. The map awareness granted by your selfless act will give you a HUGE advantage. You'll be able to avoid ganks and set up your own, and you'll be able to get back before the situation becomes dire. Your team will love you and sing your praises.

Closing remarks:
Black shield gives immunity to ALL CC, and some magic damage, your carry needs it every time you get into a teamfight.
Dark binding is not for damage. Merc Treads negate 40% of it off the top, and cleanse does too. Use it to stop people chasing you, or to catch a fleeing enemy. Let your carry get the kills, you don't need them.
Don't build AP, for the love of god. 40% of the damage on your Q is negated by a 1200 gold item that most people get anyway. Not to mention they won't sit on your W if they get out of your Q. Also, Cleanse now properly gets rid of Morgana's ult, so they don't take the stun immediately, they just run away, fat and happy.
Morgana's ult is for slowing chasers or fleeing enemies. Most people will run the moment they see that line connecting you, so use it when they're low on health so your carry can kill them.

Criticism is necessary for growth, so let me have it.

The ideea of the build seems ok. Morgana is already a great support hero (because of that fact that I main annie, I know how annoying she can be), but there are better supports out there.
AP is still good for morgana, so I think your build should be more AP-Support oriented.

Pure support Morgana is a waste. Your main support comes in the form of Dark Binding (good regardless of whether you go AP or team buffs) and Black Shield (buffed by AP). Your build suggests you die an awful lot on Morgana and subsequently focus your summoner skills and items to save you. Between Dark Binding and Black Shield Morgana should never die unless she gets herself out of position or sacrifices herself to land the 2nd half of Soul Shackle. Most of her

Rod of Ages should be the first item built on any type of Morgana. It provides survivability (HP), staying power (MP) and a boost to ALL skills (AP). After that it's up to you there's plenty of good options depending on the comp you're facing (Abyssal Scepter for caster opponents, Rylai's for melee opponents). Only very rarely where the team DPS is amazing and your opposition is all melee is something defensive like Frozen Heart viable. Glacial Shroud is okay for CDR but Soul Shroud is a waste (you won't need more HPs if you finished your RoA inside 20 mins and 15% CDR aura is situational at best--team fights are usually over before it matters). Fiendish Codex or Deathfire's Grasp are better for CDR.

Also, Morgana should always be 9/0/21. You get 9% CDR, 15% MPen, and a host of good caster utility skills. A smart Morgana with RoA won't die and doesn't need points in the defensive tree to live. Dodge Runes should be the extent of her defensive specialization IMO.

Pure support Morgana is viable if the team around you is simply amazing, but for all other possibilities, Morgana is perfectly capable of contributing some damage (she will never be an Annie or Ryze), a stronger Black Shield, and still surviving the 5v5 encounters.

EcoEco: This build has, with Soul Shroud and Frozen Heart, exactly 40%(the cap) CDR...Also, I did mention Move speed quints+Black shield as your main getaway. Ghost is there if you're outnumbered or early game. Also, I rarely chase more than one person with the ult, and you can always(unless they flash or ghost) keep up with one person long enough to get the stun.

Arcades: I have considered building RoA on Morgana, but my skill build doesn't support a whole lot of gold until you start pulling in a decent amount of assists(usually not until level 8+ when laning phase is over.) I've tried all sorts of different skill/item builds, and I've found that Frozen Heart is more useful than any other 25% CDR item(Only other one is Nashor's, which isn't very useful for my build beyond the CDR and mana regen, which is covered by Soul Shroud). Generally, I die around 5 times, but by my own silly mistakes, usually trying to snare someone for the team and overextending. On the subject of masteries, I used to always run a 9/0/21, but I get full CDR from a reasonably easy item build, don't need (or want) the Magic penetration, and the summoner spells I use have a short enough cooldown that I don't need a full 21 in utility. I like the extra points in defense for the 60hp at level 1. Lastly, the black shield doesn't need to be much stronger, since most people aren't going to eat through it before they blow CCs, accidentally, or on purpose, on your carry.

I have played Morgana quite a lot, trying lots of AP, AP/CDR/HP and all the builds in between. My playstyle just lends itself best when I'm not looking for the kills. Being able to survive, catch someone in a snare for my team, or slowing one or two people while the rest of my team cleans up is more important to me.

Double post.

how about Leviathan, crystal scepter, boots of swiftness (merc treads are for pussies...though they are nice when there is tons of CC..okay, merc if they have tons of CC, otherwise swiftness), Soulstealer, Rof of Ages and zhonya's if you feel like being a ******...this works well for me...just fire off Dark Binding, then run in, shield, soil and soul shackles...you will destroy and tank everything