In Back to the Future Part 2, it starts raining soon after lightning strikes the time machine and Marty is left stranded in the past again. Justified in that this is the same storm that played a role in sending Marty back to the future in the first film, and there were all sorts of signs of a storm brewing the whole time anyway.
Happens in a scene of the French comedy Bienvenue Chez Les Ch'tis. In France, the northern regions are caricatured as cold and ugly; the main character of this film is transferred there as a sanction for trying to fake a handicap for a job. He prepares for hell, and just as he crosses the sign of the dreaded region, well, this happens.
Live-Action TV
In Sanford and Son the pair have a disastrous camping trip and Lamont notes that it could be worse. When his father asks how, Lamont notes "It could snow." Sure enough, it instantly starts snowing right there and then.
Turned up an extra notch in That's So Raven: Raven got stuck in a limo's moon roof when going to prom. Then it started raining on her. "Well at least it can't get any worse"...cue the gale force winds.
Inverted in The West Wing, where rain was seen as a good thing that needed to happen in a string of good things happening—it turned away late voters who would have voted for the other guy, and the rain was literally called on cue by Will (with a lampshade with a "I didn't know I could do that"). It would have been played straight if it was from other guy's POV.
Also inverted in How I Met Your Mother, where Ted calls down a deluge in a massive thunderclap by screaming "COME ON!!" at the heavens after doing a desperate Rain Dance all afternoon. However, it played this trope straight for Sandy Rivers, who was going to get laid on a planned camping trip that was canceled by the rain. In fact, Sandy is seen crying while he reports on the downpour on TV.
Music
The Russian punk rock band Sektor Gaza has a song Tuman ("Fog") with lyrics that literally translate as: "We're getting the jitters/ The rain started suddenly /The stiff, pouring rain will finally kill us..."
Garfield: Here I am, stuck up a tree. Things couldn't be worse. (starts raining) Garfield: Okay, okay, now things couldn't be worse. (lightning strikes)
In another strip, when Jon and Garfield are at a picnic:
Jon: Well, Garfield, the ants ate my cherry pie. The wind blew the food everywhere. Garfield: Don't say it! Don't say it! Jon:What else could possibly go wrong?(starts raining) Garfield: You said it!
Calvin's dad: At least it's not snowing! Right? Right? (Later, as they sit in the rain eating cold ravioli out of cans.) I mean, say it was snowing so hard we couldn't make a fire.
Naturally, the rain stops the exact moment they decide to leave.
Theatre
Company, "Getting Married Today," after the second verse of Amy's nervous breakdown:
Bless this bride, Totally insane, Slipping down the drain, And bless this day in our hearts (thunder) As it starts to rain.
Subverted in an episode where the Simpsons lose their house. Tossed out unto the street, Homer says, "Well, it could be worse. At least it's not raining." (Beat) "See? Told you it could be worse."
In another episode, Mr. Burns is telling the story of how he went to jail. As Smithers leaves, Burns notes that this the point in a story where it would start raining, and decides that, since he's telling the story, it did rain. Then he decides that rain wasn't depressing enough, so he has it snow instead, capping it off with Smithers losing his nose to frostbite.
In the Family Guy episode "Brian Writes a Bestseller", Stewie is stuck without a ride and without cab fare. He says, "Well, at least it's not raining." Promptly subverted when a man runs up, stabs him, and leaves him for dead.