Galio is one of the best tanks to go against any type of team with magic resist. His (Q) and (E) together make for an amazing nuke combo early/mid game. His passive is great for this build because the amount of magic resist you build obviously increases your defense, but it also increases your offensive abilities too.
Although Galio's health isn't too high compared to some other tanks, his damage taken is low, which evens out.
I've seen a few people play Galio as just a straight up AP DPS. I'm not a fan of this because your health pool is not very big, and without damage reduction, you're pretty much useless. Your ultimate will probably get you killed a lot of the time without any armor items.
Even playing Galio as a straight tank, he is still dangerous.

6/22/11 - Edited Item Build to give you a better late game core.

x 9 - Gives Galio his much needed Magic Pen for his spells. Helps immensely for harassing early game and gives your ult a little boost late game.
x 9 - Gives Galio a boost to his Mana per 5. This is needed for early game so you can stay in your lane longer.
x 9 - Gives a small boost to your Magic Resist which helps/grows throughout the game.
x 3 - Gives a great boost to your health early game. Late game it is barely noticeable though.

These masteries are just a small variation of basic tank builds to curve towards Galio mana needs. An explanation isn't really needed. They all benefit Galio in some way.

Q

- Your main damage dealer. Is great for farming creeps and harassing your enemies. It does have a high mana cost for Galio though. The slow mixed with your E can almost ensure a clean getaway. It takes practice to hit this skill a lot, so just keep trying.
80/135/190/245/300 (+0.8 of your AP) magic damage. Small AoE.
24/28/32/36/40% slow for 2.5 seconds.

W

- Great for supporting your team and yourself for that matter. It increases your Magic Resist, which is an increase to your ability power. So be sure to use it before you Ult or want to do big damage.
30/45/60/75/90 increase to your Armor and Magic Resist. Also heals you for 20/32/44/56/68 (+0.3 of your AP). (-20% healing for each consecutive hit)

E

- This mixed with your Q makes a great combo. Opponents health can drop from full to half with just one use of this combo. It definitely makes your opponents scared early/mid game. It is also a useful getaway skill for yourself and teammates with the movement speed increase. 60/105/150/195/240 damage in a line. Speed increase of 20/28/36/44/52% while standing in the line. The line lasts for 5 seconds.

R

- This is basically an unmistakable initiative spell. Together with can catch your enemies off guard and your team can have free pickings on anyone they want since they will all be taunted and focused on you. This can be used as a great rescue ability when someone is chasing a teammate. During the mid-game phase, while defending a turret, your goal should be to use this when someone is in range of your turret. Once they attack you, the turret should shoot at them, if that doesn't kill them, it will send them back to their base.
A 2 second taunt, with a fairly large AoE. Deals 220/330/440 (+0.6 of your AP) magic damage to enemies still in the AoE, plus an additional 5% damage for each attack he suffered while channeling. Max 40% bonus damage.

Overall:

You should rank up your Q to max first. If you want to support your team more, you can rank up your W next. If you want to have maximum nukage, rank up E. Remember to always rank up your ultimate when given the opportunity.

Start out with this item always. Also grab one of each: .
You can go back when you have around 1700 gold and buy this and your at the same time. Or you can buy them separately at 490g / 1200g. Always buy your Chalice first though since it is a huge mana saver.
Armor, Health and Magic Resist. A must on all tanks to be honest. It is also an aura item which helps out your team a little bit too. Everything counts. Get rid of this late game though and make room for another heavy item.
This is basically a key item for Galio. A big push to your health/mana and magic resist all at the same time.
If you are having problems with being ganked or surviving after ulting, you should build this after your Banshee's Veil. If you're doing great and having no problems surviving, you can hold off on this until a little later.
This is a must against a team with ANY physical damage. It adds a little boost to your damage done when you're ulting as well.
An amazing item for Galio. The Magic Resist turns into AP, and there's a lot of it. So it's a huge boost all around for him with the HP regen as well.
This item gives Galio a much needed jump to his health. You can take more damage and regenerate quicker. You might want to get it earlier in the game and farm up your health bonuses. But I like to get it towards the end.

Note: Mix and match other items. Galio's build really depends on the other team's composition. If their team is 3 Ability Power champions, and 2 Physical Damage champions, this build is going to work. If it's 3 Physical and 2 Ability Power champions, you could throw in a or instead of your Force of Nature, even though it decreases enemies' attack speed, which might decrease the damage on your ultimate, the armor is a great help.

This is basically a must for Galio. When used with his ultimate, it will catch the enemy team off guard. It is also great for defense, flashing over some terrain for a clean getaway.

This is also a must. Early game you are very mana hungry, and need all the help you can get. It does get kind of useless towards end game, but early game it's a necessity.

Using and together will take down creeps at around level 10+. Before level 10 the creeps are left with around 15% health, still an easy last hit. Using these two spells will rack up your money.

Only use your Q and E to harass enemy champions until you get your since you will run out of mana quickly if you just blow it all on creeps.

and will be your main goal in team fights. Use Flash to get into the middle of the enemy team, and get as many enemies taunted as you can. It is great to initiate and let your team pick off their carries. Your assists will stack up and you might even get a few kills. Using to shield teammates who are being chased will get you many thank yous. Your goal is to protect your team. Do everything you can, even if it means sacrificing yourself. If your team is even a little bit competent, you will get love.

Galio is my favorite tank and I made this guide from playing him so much with trial and error. I play solo 90% of the time, so nobody really picks a tank, so I pick Galio. People love me for it.
His ability to soak damage and also have a big damage output makes him a great pick for any team needing a tank. Like I said before, the item build can be mixed and some items can be replaced, it just all depends on the other team's composition. It's all preference.

I'm not a big ranked game player, as I am still learning other champions in normal. My only ranked game I played, I used Galio and we won. Each game I get better, and just as a word of advice, if you like the champion, use it. You will get better with each game you play.

This is my first guide, so some constructive criticism would be helpful.

I'd like to thank Lazukin, who's build is what really got me into playing Galio nearly every game.