Not Updated For Current Season
This is the build I that I usually go as Rammus. Your job is to go straight for the carry in a teamfight, exhaust and taunt them so your team can focus them down.
Your skill priority is R>E>W>Q. You are going to max your E first and take a point into your ultimate whenever you can.
Powerball is a very useful skill. It helps you catch up to fleeing enemies and save teammates. You only need one level in this skill during your first three levels and it will be the last skill you will max. Since leveling up this skill doesn't increase the speed, the small cc, and duration, you only need one level in it. Leveling this skill up will increase its mana cost, and if you've ever played Rammus, you will know that he has mana problems.
Defensive Ball Curl
This is the skill that allows Rammus to tank. It gives bonus armor and magic resist along with returning a small amount of damage at your attackers. You will max this skill after your taunt.
Puncturing Taunt is why Rammus, in my opinion, one of the best tanks in league of legends. At max level, you can put someone out of action for three whole seconds. You also use this with your powerball to help your team catch up and get kills or just save them from ganks.
Tremors is another reason Rammus is such a great tank. Its a mini crowstorm that can hit towers. With this skill, you can drop towers EXTREMELY easily if the opposite team isn't guarding it. At max level, this skill alone can do more than 1k damage to a tower. When Rammus' level is high enough, he can use this skill to backdoor. But remember, this skill cannot hit inhibitors. It also does a reasonable amount of AoE damage.
Your core items are Boots, Randuin's Omen, and Banshee's veil.
Rammus has an extremely low base health for a tank, therefore you need items that give health and armor/magic resist.
Start out with a Doran's shield and a health potion. After this, you want either ninja tabi or merc treads depending on the enemy team, and an Aegis of the Legion. After your Aegis, get a Heart of gold. You should get a Negatron Cloak the next time you get back if the enemy team has AP damage. After this, finish your Randuin's omen for its armor and health. At this point, you are able to tank turrets effectively. If the enemy team has AP damage, (Vlad, Annie, Veigar, Ryze, etc) you want to finish Banshee's Veil. If the enemy doesn't have that much AP damage, go ahead and build a Warmog's Armor. Remember to start with the HP items instead of the Regrowth Pendant, you don't need health regen this late into the game. Finish the Banshee's veil after your Warmog's. In the case that theres around 3+ ap damage champions, you can get a force of nature with the Banshee's Veil. Normally, I wouldn't get it for the same reason as thornmail: it doesn't give any HP. When you have these items, get A funfire cape. It increases your damage output in teamfights as well as give hp and armor. You can also get an Aegis of the Legion for your team if you haven't gotten one yet. If you don't want the Aegis, get another tank item of your choice or an Atma's Impaler with your warmog's
Items NOT to get
I see a lot of Rammus' that get thornmail and guardian angel. First of all, thornmail is only worth the money if you are against a team of 5 squishy dps heroes. In any other situation, a sunfire and randuin's are enough because you have your W skill. In a recent patch, Guardian Angel has been nerfed to the point that it isn't even worth it on a tank like Rammus. Sure it revives you, but it doesn't revive you with much HP. In the time it takes for you to revive, the other team is usually around you waiting for you to come back to life with minuscule amounts of hp so they can kill you again. Banshee's veil and Force of nature is a much better buy if you want magic resist and Randuin's and sunfires for armor.
Try to last hit, save your lane partner with your taunt and powerball and help your lane partner kill stuff with your Q>E>W>R combo, and harass whenever you can. If you find yourselves getting pushed back, go into your defensive ball curl and taunt your enemies into your tower. If you ever find yourself having to recall, make sure to bring a few mana potions. Rammus has a very small mana pool. Also, it is more important that your lane partner get the kills than you. You are merely a tank and lane partner probably needs kills a lot more.
Powerball around to help your team gank, help your team push towers, and help your team tank dragon whenever they feel like killing it. Remember to taunt dragon to reduce it's armor.
When initiating teamfights, powerball in, taunt the carry, defensive ball curl, and turn on your ult. You can also exhaust any other physical damage champions. Because your taunt lasts for a whole three seconds(a REALLY long time), the person you taunt should drop dead under the focus fire of your team. Try not to be stupid and rush in blindly without your team backing you up. If you see your team doing fine in a teamfight, you can go backdoor that half hp tower thats been bothering you the entire early and mid game with your ult. Be careful of ganks when pushing alone.
Smite(if you're jungling)
Any of these spells are fine on Rammus.
These spells are not worth the slot on Rammus.