Powerball can be used as an effective escape mechanism.
Using taunt on a champion by your tower can cause the tower to attack your enemy.
Tremors and Defensive Ball Curl can be used late in the game to obliterate towers. If you're bogged down in a team fight, it is often valuable to break off and attack the buildings.
Pay particular attention to when his Defensive Ball Curl is off. Rammus has much lower stats than a normal tank when he's out of the stance.
Rammus often stacks high Armor, leaving him especially vulnerable to caster damage while not in Defensive Ball Curl.