I play Rammus when our team doesn't have a tank. For a while now Rammus has been my go to Champion.
Rammus is a Tank and I usually play him as such. Using taunt on champions that are pummeling my allies. Rammus' abilities include:
Spiked Shell (Passive) - receives 25% of his total armor as bonus attack damage.
Powerball - enters a rolling ball state for up to 7 seconds, increasing his movement speed by 30% and then continues accelerating. Upon impacting with an enemy, all nearby enemies will be knocked back for an instant and be dealt magic damage. Additionally, targets affected by the impact will be slowed for 3 seconds.
Defensive Ball Curl - enters a defensive stance for 6 seconds, vastly increasing his armor and magic resistance and returning magic damage for each autoattack that enemies use on him.
Taunt - taunts a target enemy, reducing their armor and forcing them to attack Rammus for a few seconds.
Tremors (Ultimate)- creates tremors beneath him for 8 seconds dealing magic damage to nearby units and structures each second. Rammus can move, attack and use other abilities while Tremors is in effect.
For Items I do the regular recommended Items starting with Doran's Shield, then pick work my way to Thornmail because of its passive. From there I will purchase the other recommended items in no particular order, if the current game is alot more team fights then I pick up Aegis of the Legion next followed by Sunfire Cape. But if the game is alot of laneing I will grab the Cape first.
If it is a long game and I have bought all the recommended items I ALWAYS trade Doran's shield for more armor. Keep Rammus' passive in mind when looking for more items.
When levelling up it is almost always based on the game but:
1 - Powerball
2 - Defensive Ball Curl
3 - Taunt
4 and 5 your own choice
6 - Tremors
7 to 10 your choice
11 - Tremors
12 to 15 your choice
16 - Tremors
17 and 18 your choice
Quick tip: If my team is huddled at the base defending and the enemy has a weak tower I travel to it use defensive ball curl and tremors to take it out. It usually draws at least one person away from the assault and gives your team money.
Quick tip: Due to Powerball's ever increasing speed use it early. It may take time to get the timing down but it will be worth it, at rank 5 Rammus can easily get to 700+ speed. Also powerball makes Rammus good at Ganking if you see the enemy champion is pushing a little to far get over there to stir things up. Come from behind with powerball to cut off a retreat, throw on tremors then ball curl, they will probably run away soon so use taunt and keep hitting them. Rammus can really do some damage with all abilities cooled down.