Updated to Patch v1.0.0.115
Greetings Galio lovers!
Galio was one of my first purchases, but after a few matches with him, I neglected him.
The reason I was so disappointed with him, is that I didn't understand what his proper role was.

A lot of builds I see here refer a role to champion that is not designated to it.
Take a moment to look back at a creation of a champ; someone thinks "lets make a phenomenal tank" so he create Rammus with an incredible shielding skill and a good initiating abilities (Taunt and Powerball).
While, lets say, Nasus can be a good DPS carry, but a lot of other champs can perform this role better.
When I think of Galio's skills, his Unique qualities are supporting and initiating team fights.
After I came to that conclusion my skills with him got a lot better.
EDIT: I've made many changes to my original build since the .110 patch, based on more experiance playing with him.

Pros:
-Really good harrasing and farming early game
-Good tanking (not the best) with an amazing initiating skill - Idol of Durand
-Good support; not the "I'm a healing champ with a horn on my face" type but more on the offensive side of supporting
-Team fight outcome changer
-Tier 3 champ, rarely seen on matches, underrated most of the times (makes it unique to play with him)

Cons:
-Not the best tank, not the best support, but kind of a good mix of both.
-Using Ulti in the wrong time\place will most likely cause you to lose the teamfight
-Require a certain amount of time to learn to master him.

For runes I like to take 9x Greater Mark of Magic Penetration, 9x Greater Seal of Scaling Mana Regeneration, 9x Greater Glyph of Scaling Magic Resist and 3x Greater Quintessence of Scaling Cooldown Reduction.
As for CDR\lvl, this is a preferable choice, besides, It is a good affix for every champ, making it a good investment for overall playing LoL.

As a tank-mage(tank being before mage) I like to get as much survivability as possible, with the little perk of AP and Mpen from the offensive tree. Standard 9/21/0 with emphasis on MR+'Spirit of Strength', armor and health.
Note; I'm skipping Ardor since I wont stack a lot of AP anyway and I don't really need the extra AS.

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As for my Summoner spell, I've picked Flash and Heal. I've suggested Ghost before, but I've noticed that with my Righteous Gust and the edited item build, speed is not my problem, while Flash can save your ***, save your ally's *** by jumping to him with Heal and, if necessary, Ulti (This happens to me at least once per game).
If you're not the Flash type, Ghost would be my next choice - Flash might not be enough to get close to the enemy team's players for your Idol of Durand, while Ghost lasts for some good several seconds, you got more time to set your position for the Ultimate.
Alot of people dismiss Heal right away, but when it comes to Galio, I can't find a more suited spell. Unless you've got a healer on the team ( Sona, Soraka etc.) heal saves yours and your allies's lives at least twice in a game (not including early game phase!) it counters ignite very well, even with the 50% heal reduction because you only need to survive throughtout the ignite. If you are still in enemy's range, don't bother wasting heal.
Second best suitor for Heal would be Exhaust

I've made a complete change to my build, since I discovered Shurelya's Reverie!
Start off with Doran's Ring. Doran's items are really good since their affixes to gold ratio is great and it takes so much time to actually need the room they take in your inventory, its just a really good starting item.
Try saving enough for the whole Philosopher's stonePhilosopher's stone. If you cant try to make it at least for both items or Regrowth Pendant and Boots of Speed. The reason I've replaced Shurelya's Battlesong with Chalice of Harmony is that while all of Shurelya's Reverie affixes are great throughout the game, Chalice of Harmony becomes pretty useless in late game since your mana regen is high enough to sustain your skills and in early game the % mana regen is profitable only when you mana is on 0!
the next items are as mentioned above, I won't suggest when to go back to buy, I think everyone has their own preferences.

These are your core items. As for the rest of the items, I'm always counting the number of mages\physical on loading time and then decide what to buy. if they have 2 physical champs or more, get Randuin's Omen. it has been nerfed in the last patch but is being un-nerfed in the next so out of all the armor-based tank items, I believe this one is the best, especially for Galio.
If you can remember to use it after your ultimate breaks off, it will significantly tip the scales to your favour. for 2 physical champs 1 Randuin should do the trick. if they have more, consider Frozen Heart or Sunfire Cape. If the enemy team is mainly mages, well, you can just go and have fun.
If your team has a lot of mages, or you've got another tank, Abyssal Scepter can jump your AP by 100, your Magic resist by 57 and support your team with the MR Reduction aura.

**If the above build is not to your liking, I've left the old one here as well**

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Start off with Meki Pendant, 1 health and 1 mana potion.
If you are not being harassed much, save enough money for Chalice of Harmony and Boots of Speed (850) and call back. If you are getting harassed a lot and can't farm or get XP, call back as soon as you can afford Chalice (500 gold).
From now on, you will have total domination over your lane. Now it's your turn to get aggressive; harass your opponents or farm as much as you like. As soon as lvl 4/5 your RS+RG combo will kill the mage minions, allowing you to push very easily. The best thing to do is wait for the enemy to go into the minions and then cast your spells. this way they will constantly have low health percentage and you still get the gold from the minions "Two birds with one stone?". When your minions get close to the enemy tower, use RS and RG to prevent the enemy from last hitting and restoring HP. doing so is fairly easy since you can do it from far away without taking the risk of getting the tower's aggro.
Next items are Mercury's Treads and Negatron Cloak for Banshee's Vail. The reason I made this item the core, is because it will perfect your ultimate. even if they have more than one champ that can force you to stop Idol of Durand, most odds are that you capture the other one inside it! Back to where we stopped, I prefer Negatron over Catalyst because it gives me more harassing power and I don't really need the health and mana regen because I use defensive masteries and Chalice, so I've got both of these covered, plus I usually control my lane from afar, and so my HP remain high.
After you get your core items (the three mentioned above) it all comes down to the enemy's team and YOUR team. Keep in mind that you are a support-tank (in other words- double sucker), so if no one takes aegis, you may consider buying it yourself (yeah, you are a double sucker).
Now take a look at your and your enemy's team, If you've got 2 or more AP champs, you might want to get Abbysal scpeter (yeah its great for yourself too!)
if not, keep stacking armor\MR\Health
my choices are usually Sunfire Cape or Glacial Shroud (I won't upgrade it to frozen heart yet)
Other Items to be considered are:
Thornmail: (against a HEAVY physical team - 4/5 champs or 3+ if they got very strong AD Carries, such as Tryndamere, Ashe and so on)
Randuin's Omen: Although Thornmail is really sweet, it is more viable to get Randuin's Omen (again, you are a TANK-SUPPORT)
The problem with this one is that people often forget to use the active function, which makes this item so incredible. Cast it right after your ulti to finish them off.
Spirit Visage: Good cooldown, good health and stacks nicely with Bulwark. I will take this item only in case There is another healer in my team, or if I'm overfed (I like this item so much!).
Force of Nature: Great for Galio, but I find Banshee's vail and Abbysal scepter more useful and more than enough. purchase this one if they have more than 3 AP champs (Lets say they have 3 AP, 1 AD and Malph as a tank, I would get this one since Malphite's skills are mostly magic, same goes for Rammus)

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Casting Idol of Durand:
You must make sure your team knows you are about to cast it!!! Dash forward with Shurelya's Reverie (try to use it in the middle of your team) and try to take in as many champs AND MINIONS as Possible into your Ultimate. Minions also trigger the auto-attack counter, so getting more creeps inside means getting the maximum effect from your Ultimate while clearing the way of creeps.
IMPORTANT: It is best to save Righteous Gust and Resolute Smite untill after your ultimate, for a few reasons:
1. After your ulti is done, most likely there will be a cluster of enemies around you, cast Resolute Smite on them for maximum effect.
2. Shureliya's Reverie can help your carries follow suit, and they will be there in time untill your ulti is finished. Now you can decide if this is going the way you planned or not, in any case, use your RG in the direction you think will be most useful; chasing the enemy running away!

On a side note, casting Bulwark on an ally that kills an enemy champ gives you an assist, even if he dies from DoT spell, and since it has a nice range, make sure you cast it before that enemy dies incase you are far from the fight, and get a sweet reward for free :)

Galio is fun-to-play and very viable on a team and one of the most fun to play tanks.
Hope I helped this community to get a little more understanding about this champ.
The above guide is a personal preference of mine and can be played differently.
Please vote after you have tried this build in-game.
Comments are welcomed, as long as they are constructive.
My apologies if there are some grammar mistakes, my main language is not English.

So if you like the role of a tank or a support, this Gargoyle is for you.

Shalom<->Peace
Amihai