Seems like it’s almost a bit of cliche and has been done many times, but I can’t picture the movie.
Indiana Jones?
In fact Spielberg has a shooting star in a lot of his movies.
Stardust?
Local Hero?
Little Prince
ET
Titanic.
Imitation of Life.
Armageddon?
I think it happens in Dances with Wolves?
It’s been a very long time since I saw it but ISTR there is apparent star movement in Close Encounters of the Third Kind, but presumably they are actually UFOs and not stars.
There’s a shooting star in Return To Oz (though it turned out to be a key to a door in Oz)
Platoon
Disney’s “Chicken Little”
There’s a shooting star in Jaws, but nobody’s looking up at it.
There are some shooting stars in Close Encounters, but as mentioned above, Spielberg seems to put them in most of his movies.
An American Tail. About 30 seconds into this YouTube clip, as a matter of fact. Warning: High degree of cuteness.
Pinocchio?
When you wish upon a star…
Sweeney Todd? “Oh look, Joanna … . a star! A shooting star!” (SLASH! kerTHUMP!)
Heh. Just thought I’d add a somewhat darker version of this saccharine cliche. (Actually I haven’t seen the film version yet, maybe this line’s not in it…)
Also, in Contact, little Ellie sees a bunch of ‘shooting stars’ (during a meteor shower) right before she hears an ominous thud from inside her house… where her dad’s just died of a heart attack.
The end of Jason X.
Isn’t there one during Gonzo’s song in The Muppet Movie ?
Armageddon and Deep Impact. 
The shooting star is kind of a Spielberg trademark. Kind of like John Woo with white doves and guys jumping through the air whilest shooting two guns screaming “YAAAAAAA!”