Hello, This is my Nunu build.
Nunu is an amazing charaster for everything! He is very great at farming, nuking, chasing, working with team mates. To play a successful Nunu Tank I suggest you follow this guide.

First off Items:
At first you will get the Null-Magic Mantle. The reason I say get this first is because you will have some sort of champion who will use spells on you because you're the big Nunu nuke. Later on you'll get the Mercury Treads because the reductions on it will save the day from time to time. Plus you wont be dying and this will help. After the boots you will want Chain Vest then you will use that to go into the Guardians Angel. Once you have Guardians Angel you will not die again from that point on for the rest of the game. After this you will want to get all of you basic items for a excellent tank. Such as Thornmail, Force of Nature. After you have these two items will have enough defenses to get some health now. If you get Rylai's Crystal Cepter it will make it so that you can have health and ability power. With the ability power you will be able to hit for a bit more plus your spells will slow them even more! After that getting a Warmog's Armor will make you have a very high amount of health and very great defense with still great DPS.

Spells:
Visionary: This is Nunu's passive. This is the most amazing passive in this game. You will want to wait for this to be up then taunt your enemies or to nom down on some minions. This will keep you at full mana early game making it very easy to have no need to go back.

Consume: This spell is amazing for laning. You can use this spell for jungling too. This will actually make it so that Nunu can stay in a lane solo such as if you have a WW or someone jungling. This spell also makes it so you are not harassed. Use this when Visionary is up and you will not go OOM and you wont go low on health.

Blood Boil: This spell is kept at rank one till its the only thing to max. The reason for that is that you use this to chase and run mainly. That is about it. When your chasing make sure to use it on your team mate so you both gain the speed, same for when your running. This spell + Ghost will get you out of a lot of trouble.

Ice Blast: This spell is going to be the main thing you max right away. This spell is an AMAZING slow. Also it is an amazing harass. You can actually use this spell to keep your enemies under leveled if you use it correctly. If your chasing dont forget to use it to slow them down.

Absolute Zero: This spell is the most powerful ult in the game. It is easily countered though. This spell if used correctly will win your team a team fight every time. This also has a 250% AP Ratio which will help you insanely with the lowest amount of AP possible. Also its CD is low if you have Golem.

Summoner Spells:
Ghost: This spell will help you in chaseing if the enemies are barely out of range of your Ice Blast. Use this to escape the ganks where there are no MIAs either.
Heal: I use heal because it is amazing when everyone targets you during your ulti and you can use your heal to actually negate all the damage they did and then explode them aswell.

Early Game: During this time you will want to focus on mainly just using your Consume on the minions to gain gold and also keep yourself at full health. Make sure that you have Visionary on so you wont loose mana till you need it. Usually early game will seem the longest but it will be easy to stay in lane without having to go back. Usually when I go back for the first time I have around 2000 or around 3000 gold but I have maxed at 4700 before I had to go back.

Mid Game:
This is when people will usually start trying to gank. What I have to say is only go to help your team if they really need it! DO NOT GO IF NOT NEEDED! When people try to gank you..... well that is when you ghost and blood boil yourself increasing your movement speed by around 65% which is enough to get you out easily. Also if your running and they are chasing remember Consume. Run through the jungle and nom down on some of the monsters this will be a life saver. Around this time you will be getting your FoN and then your Crystal Scepter. Nunu's defense will make ganks very difficult when you have around 250 armo and 180 magic resistance.

Late Game:
Late game is when Nunu is at his best. Nunu will have huge defenses and also he will have a ton of health too. With all this he will not die and remember you bought Gaurdian's Angel for a reason. Use it to your advantage.

About Nunu:
Nunu is a very good Tank for on huge reason! People fear him! No one wants to get stuck in the middle of his ultimate. That thing actually causes you to have a theoretical all time taunt. People will want you dead because that thing hurts everything within range. Also be aware that Nunu is labeled as just about everything you can think of. That is because he can be used in so many different ways. Make sure you play Nunu correctly and you will be unstoppable.

Sorry if this was too long which I doubt it is. I know you do not see many Tank Nunu's or even Nunu's in general but I hope that this guide will inspire you to try him out and succeed.

I hope this guide was helpful and I explained what to do and use. If you have any questions let me know in the comments and I will answer them.
Yours Truely,
eQuality77