Puddles was not housebroken, and would often piddle and leave puddles everywhere when he would get nervous or stressed. Because of this, he was worried that his perfect person Sam would not want him. The worry grew so bad for Puddles that he ran away to a fountain- if he had an accident in there, nobody would notice. Ultimately, though, Sam loved Puddles and did not mind that he was not housebroken, and was willing to help him get through it.
Another trait of Puddles is that he likes to dance. One time, he danced to celebrate piddling on the appropriate pad, another when Sam played a dance video that he and his parents used to dance to.