Rammus is a very good champion right now, with Banner of Command and Zz'Rot Portalbeing quite strong at the moment, plus Grasp of the Undying helps out the problems with sustain he used to have. He just demolishes structures, wrecks teamfights and becomes impossible to deal with; only exceptional duelists ( Trundle, Olaf, Shen, Master Yi, Nasus) and insane peel ( Janna, Lulu, Morgana) can deal with him. He also has exceptional waveclear with every single of his abilities + the items you build.

9x Greater Mark of Attack Speed
9x Greater Seal of Scaling Armor
9x Greater Glyph of Scaling Cooldown Reduction
1x Greater Quintessence of Scaling Cooldown Reduction
2x Greater Quintessence of Armor
Run this page every game. Don't trade early as much and focus on late game when you will be massive. Once the cooldown reduction and armor starts coming online you are a MONSTER. Some people run hybrid penetration instead of attack speed marks. It only helps vs champions and not structures, whereas attack speed helps in both instances so I'd say no. Also instead of cooldown reduction some people run scaling or flat magic resist. Again, I've beat mages top lane because my Defensive Ball Curl + Bami's Cinder damage early game is way too much for them to handle. Magic Resist can easily be itemized for... cooldown reduction is another story.

Doran's Shield An item to make laning easier vs your counters. Buy it on your first back if you're not allowed to farm freely.

Sunfire Aegis is a really good rush and it's typically my first item in every matchup, even against AP. The magic damage plus scaling on your Defensive Ball Curl is too good to pass up.

Thornmail Typically my second item in AD matchups because it makes you impossible to kill, gives you really good waveclear, and synergizes with the rest of Rammus's kit. Plus the "bonus armor" component of Thornmail applies to the resistances gained from Defensive Ball Curl. Get this after Zz'Rot Portal if you bought it second.

Zz'Rot Portal A good second item in AP matchups, it helps you match their pushing power and gives you a good amount of magic resist to withstand their poke. Buy it third if you bought Thornmail second.

Banner of Command Okay let's get into the guts of this item. Why are we building AP on a tank? Every stat on this item is really good for us. Cooldown reduction helps you spam Puncturing Taunt more often. Health and Magic Resist makes Rammus withstand more blows. The Legion passive is useful in teamfights. Rammus also scales quite well with just a bit of AP. Powerball scales 1-1, and Soaring Slam scales with 240% with your AP. Factor in Dragon and Baron multipliers on your AP and that adds up a lot. Not considering its passive + Zz'Rot Portal is ridiculous for split pushing.

Boot Options:
Boots can be bought at any time. For instance, Ninja Tabi is a good rush when you're getting outdueled in lane, but can be bought as late as your third item if the lane was easy. It's hard to explain to someone, play a few games and you'll start to learn when to buy boots.

Ninja Tabi: Only buy if you're getting outdueled.

Mercury's Treads: Pulling your hair out at the enemy team's Morgana and Janna? Buy these and your hair may remain on your head. Well maybe. Depends on HOW much you hate them.

Boots of Swiftness: Sell them late game for Ninja Tabi or Mercury's Treads, but they're a great rush for roaming and split pushing. Also good if their only CC engine or form of kiting is Blue Ezreal (which happens more often than you'd think in solo queue).

Also never sell your boots on Rammus.

Sixth Item choices:

I don't end up getting to sixth item often, but when I do, I stop and think "What do I need?" Typically I'll look at their whole team comp or a core problem I'm having.

Void Staff: I don't buy this item often, but when I do it is solely because I need to kill fatty Gragas or Urgot faster. If the enemy team poses little threat to you and they are stacking magic resist, buy Void Staff.

Banshee's Veil: One Dark Binding or Whimsy can halt your approach entirely with Powerball and make you a sitting duck and put you at a spot where your health starts getting whittled down. Get this and stay in the fight for longer.

Randuin's Omen: I typically buy this item if they have a crit intensive AD carry like Caitlyn, Jinx, Lucian, etc. and they have a Yasuo or some laner/jg who builds crit. For most cases however, Dead Man's Plate is better.

Dead Man's Plate: A great item, it is usually my sixth item for most cases. It is a bit overrated in my opinion, many Rammus players I see rush this item and that's not optimal. It's best to get this when you're being kited or don't need one of the other three items listed.

I'll list all the Rammus items I've seen in soloq and why they are bad.

Locket of the Iron Solari: As Rammus you are not out to support your team. Most of the time, Rammus should be balls deep into the enemy team while he lets his carries kill the rest of the champions in safety.

Warmog's Armor: Rammus is a resistance tank. This means he likes to (and scales off) building resistances. Every item on my build either scales damage or greatly improves tankiness. The trade off from building this item is simply never worth it. Feel free to build this on ARAM, Soraka, Dr. Mundo, Tahm Kench, and Shen but not Rammus.

Titanic Hydra: Just no. Rammus already gets enough AD from his passive. Hydra is quite frankly overkill and a bad item in every case because again Rammus doesn't like health. Surely, some of my items have health in them, like Sunfire Aegis and Banner of Command. But the trade off from Cape and Banner is worth it, while Hydra grants no resistances and a small spike in AA damage. Don't buy this item.

Wit's End: An underrated item on Guinsoo abusers like Irelia, Kayle, and Kog'Maw imo, but it doesn't fit Rammus. The mix of stats is compelling, but other items beat it out. The magic pen is outclassed by Void Staff, the magic resist isn't as useful as Banshee's Veil, etc.

Abyssal Mask: This item is often the one stop shop for mages who need magic resist, but Rammus isn't a mage. Very similar to Wit's End in that it grants damage and magic resist but again, it's outclassed.

Zhonya's Hourglass: Are you kidding me? The active is basically useless, hell even detrimental because YOU ARE A TANK. You WANT to draw attention to yourself. This is done through split pushing and continuously killing people. 1v1ing or even 1v2ing people is infuriating. It tilts the enemy "WHY ARE YOU FEEDING RAMMUS!", and makes them WANT to kill you. Zhonya's reverses this "KILL ME" effect. Not to mention, the item is expensive as hell and minimally increases damage.

Take Defensive Ball Curl level one unless invading and need to secure a kill with Puncturing Taunt or you're caught in a really bad spot for some reason and need Powerball to escape. Two instances happen in lane. You get into a level one trade (which you will win vsmost melees) or you get harassed by a ranged opponent in which Defensive Ball Curl's extra resistances will help you survive against. If you win the level one trade and want to keep the pressure on, take Puncturing Taunt level 2 and go on the offense. Powerball is best if you're in a bad lane early like Quinn or Vladimir as you can get ganked or all-inned and need to escape.

Max R-W-E-Q. A few points into Powerball help if you are splitpushing a lot so you can escape.

Passive:
Spiked Shell: An underestimated part of Rammus's kit, it's what makes him so good at ripping structures to shreds. It's always funny to hear in /all "Why do you have 200 AD Rammus?".

Q:
Powerball: Your main mobility and engage spell. Couple it with Teleport and Homeguard and you are one speedy and scary armadillo. A cool trick to know is that you can "inSec" your opponent slightly with this ability. The way this works is that Rammus can flash at any time during Powerball. Since Powerball knocks back people depending on where Rammus was, you can actually position an enemy to get a way easier kill when done properly.

W:
Defensive Ball Curl: Your main source of damage and tankiness. This ability is quite straight forward, turn it on to give yourself extra resistances and hurt enemies when they attack you. Always make sure you use it with Puncturing Taunt as well.

E:
Puncturing Taunt: Your main source of CC and Rammus's signature spell. Remember that Black Shield and Banshee's Veil will block it. Tenacity will lower its duration, Cleanse Quicksilver Sash, and Mikael's Blessing will remove it. Something to know about this spell is that it can be used like Ahri's Charm. Sort of. When a champion is commanded to attack a target it either attacks it OR or it moves into range to attack the target. Taunt the opponent then walk backwards so they have to move into AA range. When done properly, you can actually slightly pull the target towards you. Normally you want to stay still and let your AoE damage plus your autos rip them to shreds but this trick does have its uses. Especially useful in TP ganks when you need to close distance on the enemy bot lane.

R:
Soaring Slam: A useful wave pushing tool early and not that much of an ultimate. Rammus is a QWE tank who isn't known for flashy ultimate initiations. So use this with impunity and always use it when you need to kill towers fast (because it works on structures). The damage is also good when you use Puncturing Taunt on someone.

3/9/2016 Clarified how to use Puncturing Taunt like Charm.
3/8/2016 Added "Bad Items" and started to fix grammatical errors or unclear descriptions that hindered guide.
3/7/2016 Guide was started!