I will try to answer your question into two parts
Part 1: When we assume gods are like us.
When gods are assumed like us , they can do anything like us.They play sports http://en.wikipedia.org/wiki/Lila_%28Hinduism%29 indulge in wars etc.
Puranas are based on these assumption. Here we assume that gods are just like us. Hence we involve them in stories and give them anger, lust, greed etc. This is how a lot of purana stories got evolved.
Example : Indra lusts, war between Gods and Demigods as mentioned here http://en.wikipedia.org/wiki/Hindu_mythology#Wars_between_the_gods_and_the_Asuras_.28Devasura_Yuddha.29
But the drawback or narrow mindedness here is why do we think Gods are like us Humans? Humans cannot perceive anything beyond third dimensions. But that doesn't mean that other dimensions doesn't exist. Hence when we think gods are like us, we are putting a limit to their infinite power. Hence these puranas are for moral ethical education rather than reality.
Part 2 : According to Vedanta Philosophy
Here we believe All gods are just different names and forms of ONE SINGLE god. And Vedas call him Nirakara (No akara or No form). If he is nirakara, then we cannot perceive what he does all the time. Moreover according to Vedanta philosophy of Advaita, he and us are same at Nirvikalpa Samadhi state. (When seer and seen are ONE). Hence that awareness is none other than us. Hence the above questions do not arise.
Then why do we pray to god's form(like photographs) in our homes or temples? Because normal human brain cannot perceive something like nirakara or advaita. to understand them we need spiritual maturity . Hence they say find a guru to know these. Until then start praying for these forms.