I would avoid any complication between family members due to incest, murder, or any other intrigue, so that leaves me precious few classical European gods to choose from. At any rate I would demand constant change and would spend most of my time dismantling human paradigms just to see what would come next (assuming that I am involved with human affairs; maybe [probably] I oversee an alien planet or planets). I would also be elusive to whatever conscious creatures I interact with, and would not allow them to make icons of myself or any other god, and I would smite their leaders every so often just to force a new system of government to emerge. All this to appease my curiousity about how many kinds of ways a conscious race of beings can rule themselves before reverting or collapsing. If my experiments lead to a radical type of leadership that proves resilient even against my godly treachery, then I would take that race into the deep of space where I will send them into bloody war against other races, peaceful or violent. This can go on until my people are overcome by a mightier people or sink into complacency. After that i start the cycle again.
I know that this type of thing happens quite without the interference of a god but I would just help to streamline the process a bit.