"A fork fell off the table."
Translation:Widelec spadł ze stołu.
"spadać" is the basic, literal word. Something was placed somewhere high (like, let's say, on a shelf) and it fell from it.
"padać" is used with rain/snow/etc. ("Pada deszcz" = "It's raining", but literally "The rain is falling"), and it can be used in some more... poetic contexts, like "Żołnierz, ranny, padł na ziemię" (The soldier, wounded, fell on the ground).
There's also "upaść". This one also works for people falling on the ground, just less poetic, it's also for contexts like "The city has fallen", and for when you drop something on the floor ("Upadł mi widelec" = "My fork fell"). The last one could use "spaść" as well, though.