I choose heavy utility masteries for Galio, with an emphasis in health and mana regeneration. This allows Galio to have more staying power in a match, which has a psychological affect and intimidates the other team. Towards the end of the match, this Galio build will help him to simply NEVER DIE unless all five on the other team focuses him. This allows Galio to become a true tank later on in the match, which in turn allows everyone else on your team to focus on killing and not surviving. It also allows Galio to be last in lane for a retreat while squishier characters are able to run away, thereby cutting down on total team deaths.

Health regen really helps during Idol of Durand, Galio's ultimate. Galio taunts the other team, and while they are wailing on him, Galio regenerates some of the damage dealt to him during this time. If heavy armor were built on Galio, he would have the same health at the end of his ult as he would with health regen, except the total damage taken would be much less. Since Galio deals back damage taken during Idol of Durand, you want him to take as much damage as possible while keeping alive. I choose Heal as one of my spells, because I usually heal halfway through Idol of Durand, which allows Galio to take even more damage. If used at the opportune time, Galio's ult can usually kill one or two of his attackers.

Galio does magic damage to opponents, and 50% of his magic resist stacks into ability power (AP). Once health regeneration is taken care of somewhat, I build items that have magic resist, which not only makes Galio a better tank, but makes him a more powerful mage as well. Mercury's treads are great for Galio, because not only do they cut down on slows and stuns, but give him magic resistance and therefore AP as well. Force of Nature happens to have both health regen and magic resist...perfect.

If you like characters that run into a fight and take names, Galio is not for you. Galio is patient, cautious, slow, and then becomes very powerful.
I usually get Regrowth Pendant first, because it helps staying power early game. This way, Galio only has four health bars, making him VERY squishy early on, so be cautious early game. Galio is also very, very slow without boots, giving more reason to be cautious. As mentioned earlier, Mercury's Treads give Galio the most bang for your buck.
After laning for a while, and depending on how long you've been able to stay out there, I work towards Warmog's Armor purchasing either Ruby Crystal or Giant's Belt next after the Regrowth Pendant. This makes Galio slightly less squishy, which is mostly great for its psychological affect on the other team.
Get Warmog's first (after boots) because Galio's health will increase every time he kills a minion, thereby making it a great early game item.
Next is Force of Nature, which will help both health regen and magic resist, making Galio a slightly better mage mid-match.
Spirit Visage boosts the other two suits of armor, and gives a little cool down reduction as a bonus. This lets Galio spam his abilities a little more, giving him a more powerful offensive presence.
Matches usually end before I am able to get more than these three suits of armor and boots, but my fifth item is usually Frozen Heart. It slows enemies when they attack, which helps the team in general during the team fight stage later game. It helps with Galio's cool down reduction, but is mostly purchased for its affects on team fight, not for benefits to Galio specifically.
If the other team is purchasing a lot of magic resist, Void Staff is a good late-game item.
Guardian Angel is useful, though I've found not essential. The real trick is always to not die in the first place! :-)

Always max out Galio's ultimate, Idol of Durand, whenever possible.

As a defensive player personality, I personally choose to stay back and spam Galio's range attack, Righteous Gust. I've gotten so many kills from retreating enemies by maxing out Righteous Gust. As a second priority, I choose to max out Absolute Smite. Using Absolute Smite first on an enemy and then throwing on Righteous Gust can deal quite a bit of damage when used in combination.
Bulwark is a great spell early on if you really know how to use it, but I've found it's really best late-game when SOMEBODY needs to dive that turret, and it might as well be Galio. Once the turret is dead, I usually pull Galio's ult at that point, and get all the turret defenders to attack Galio. Once released from the ultimate, use Absolute Smite and Righteous Gust to skill shot all those weakened turret defenders. BAM.

I love to be aggressive while being defensive, so I run out of mana like hotcakes early game. As a result, mana regeneration runes (Seals of Clarity) and Clarity spell are my friend. Glyphs tend to be magic resist, which helps with Galio's AP. Marks of Insight for obvious reasons. Quintessences in mana regen help me personally, because of my tendency to spam abilities. However, quints in magic resist or magic penetration might help you more if you have a different attacking/defending personality. If you feel Galio is just too squishy early game, feel free to get straight health quints.

I am no professional player, and I'm SURE there are ways to improve this build. However, as Galio, I have been able to get many more kills than every other Galio I have ever faced. I usually always have a 3-2-6 ratio, which is pretty good for a tank. Galio will die, as will all tanks, but usually Galio can get a few kills in the process! He is a great team tank, especially because his ultimate taunts in dire situations. Galio rocks, you guys. (Haha, get it? Because he's a gargoyle. Yuk yuk yuk...)