Incredibly Inconvenient Deity

So you found God. No, the actual, physical God. Turns out He wants you to do His bidding. Now, surely said bidding will always be reasonable things like, say, working as a volunteer in a soup kitchen, which earns you good reputation and - while it might be a bit of a burden on your time or money - won't consume your life, right?

WRONG! Turns out God wants you to behave outrageously, summons you at the worst times possible and sometimes even causes effects that will be very much of a burden on you, leading to losses from your reputation to your job or even your spouse! Oh, of course, this tends to solve itself, what with the Omniscient Morality Licence, and All Is Well That Ends Well. But the Almighty will NEVER make things easy on you. He WILL make you grow a beard all of a sudden. He WILL tell you cryptic stuff and tell you to Figure It Out Yourself. He will never tell you why or how setting fire to a box full of kittens on national TV will make anything better, but he will force you to do it anyways, your presidential campaign be damned! In short, you can expect any Physical God that chose you as their envoy to disrupt your life as much as they can (and they are omnipotent...) for the benefit of the audience.

Film

 * Evan Almighty. The beard example comes from there and is particularly jarring, given that it had no practical purpose whatsoever. Then there are the MANY birds entering Evan's office through the window.
 * ...which, of course, is a sequel to Bruce Almighty, where the same God simply dumped all his powers into one guy just to show him how tough God had it.

Literature

 * Depending on your views of The Bible, The Bible has stories very much like this - especially if you consider that many of the Christian values lots of cultures have now were novel - to say the least - to the people of that culture.
 * Justified in Small Gods, where the Great God Om lacks the power to do things in a way that would be at all convenient for The Chosen One, Brutha, because Gods Need Prayer Badly and it's gotten to the point where Brutha is the only one who actually believes in him.

Live Action TV

 * Joan of Arcadia. The title character had to, among other things, destroy works of art and re-take a test she had aced.
 * Journeyman hinted that the character's time jumps were for a purpose. They were seriously inconvenient, and he could disappear when driving down the road, end up without clothes in snow, etc.

Video Games

 * Daedric quests in The Elder Scrolls series of games can get this way. Kill a bull netch with a fork to please Sheogorath! Fake the apocalypse for Sheogorath! Cast a spell of mass disrobing at a dinner party for Sanguine. Commune with Boethia at his shrine (on the sea floor). Kill and soul-trap one member of every sapient race for Hermaeus Mora. You are not repulsive enough to worship Namira. The Shivering Isles expansion to Oblivion takes this to the next level as you travel to the plane of Sheogorath (where attempting to grow a beard attracts divine punishment).

Web Original

 * Thalia, Muse of Comedy in Thalias Musings. In exchange for comic inspiration, she orders a playwright to perform a series of tasks designed to annoy her totally-not-love-interest Apollo.

Western Animation

 * God and the devil in God, the Devil and Bob.

Other

 * Some theologians use this as a solution to the problem of theodicy. The existence of evil is something for us to overcome. Natural disasters and diseases and suffering are so that we can grow as people. It builds character.