Like most Rammus builds, I focus on Armor > Health > Anything. I play an aggressive tank role, depending on my team to finish off the enemy. I don't strive for killing blows, as assists are sufficient enough with the new Defense Mastery, Mercenary, to supply ample gold for my items.

Utilizing Rammus's passive, acquiring high armor value not only ensures your survival, but it also will pose you as more a threat to the enemy, encouraging them to focus you (which makes your job A LOT easier).

When playing any champion, if you're chasing an enemy, be sure you are constantly sending the move action (Default: Right Click) instead of relying on auto-path to get you to your destination, if your target leaves your sight (bush or FoW) your champion will stop, allowing the enemy to move that much further away from you. Also, as mentioned below, if at all possible, use your Powerball ability to knock your targets int he direction they don't want to go. Make an effort to get behind them and force them into the fray for battle. Flash makes this simple, by allowing you to flash through your target, or by flashing through a wave of minions instead of circling around and wasting time.

Another key factor to note is that Rammus is basically worthless without mana, so try not to waste your mana by using abilities on minion waves and harassing, especially early game.

Purchasing items is highly situational. If your versing a team that has high physical damage and low magic, you may want to substitute the Force of Nature for another health or armor weapon.

Where I suggest you should buy the Heart of Gold, I also suggest that you should sell the Doran's Shield either now, or if gold gain is slow, when you no longer have room for it (again, situational).

Force of Nature is great for Health Regen, Magic Resist and specifically Movement speed. This extra 8% should give you ample time to position your Powerball attack around a wave of minions and behind the Enemy Champion to knock them away from their escape (be it turret or alternate pathing/bushes).

I suggest the Atma's Impailer, because once your Warmog's builds up a serious amount of health, your basic attacks (as well as the boost from your armor, and damage return from TM and Defensive Curl) will put even more pressure on the enemy team, and should help cut down a single target before the taunt duration is even over.

If the game actually lasts long enough for you to purchase all of these items, you should be virtually unkillable, and act as a mirror, returning damage faster than they can deal it to you.

I play Rammus aggressively. It is important that your let your team know what your motives are, so they don't leave you to die, or over-extend. I use the in-game pings for this, as well as chat and since I don't play with randoms, it's become second nature, and just by my actions, my team can usually understand my motive.

Early game Rammus is fairly useless. I get Powerball first because it allows for a knock back, and a 3 second slow which helps catching the enemy during the initial gank. It's also incredible for escaping if you get focused. During laning, I'll use bushes to charge my Powerball up fast enough to get around the enemy before they can react, knocking them toward my minion wave and assisting teammate. This gives us more time to get auto attacks on the enemy, and i'll save my taunt for the enemy's retreat, instead of using it instantly like I see many Rammus' do. Doing this usually prevents escape, or at least forces them to return to their base (restricting Exp and Gold gain from minions, as well as allowing us to freely damage their turret).

Once the game progresses to the point where staying grouped is more important than laning due to coordinated ganks, I use a teammate as bait in a lane, jungling while I wait, then roll in to secure kills. Turrets are not an enemy after you acquire Warmog's, and as long as you don't let it attack a teammate after you build up it's damage, you can stay under for the majority of the team fight.

Because Rammus' early game is slow, getting the last kill on minions is important if you aren't getting numerous champion kills/assists. Instead of just auto-attacking the nearest minion, strafe around and actively attack for the final kill. Because of Tremors' short cooldown, I use it on large waves and every turret siege if possible (It's relatively low damage makes it expendable and is not required for team fights).

Another simple effort I make is attacking enemy minions without the aid of mine. This forces them to attack me, and with defensive curl and Thornmail, they practically kill themselves before my minions arrive and get the last hits.

Despite common belief, Rammus can be countered, and is relatively easy to do it.

With all Tanks, the purchase of Madred's Bloodrazor makes cutting tanks down easy. By increasing each autoattack by 4% of Rammus' max health, if you didn't have any health regen, you could be killed in less than 25 hits (12 seconds to a single Yi/Jax or other fast attacking champion). This is why the health regeneration from Warmog's and Force of Nature is so important. This allows you to regenerate health during combat, slowing your rate of death even further.

Deathfire Grasp is also a notorious Tank-killer, dealing 30% current health instantly (+3.5% per user's 100 AP) can be devastating. Knocking you down a 3rd of your health can turn the tide quickly, and more than one enemy can use the item. This is harder to counter, because it's instant damage. Your only defense against it is magic resist, and this still can produce negligible results.

As for other counters, a Banshee's Veil can prevent the taunt, but if you're fighting the enemy 1v1, you can use powerball to remove the veil and follow with a taunt if necessary.