It entirely depends on the application's role. If it's used in a video game with no save slots, where a crash is just going to lose lots of progress, I'd rather attempt to keep going even if there's an error, but only in release builds. Crash in debug builds to try and alert the programmer. If it's used to save important work, where the bad divide could lead to data corruption, it's probably better to crash than risk…
We have two Mars rovers right now, Opportunity and Curiosity. Fittingly, these use PowerPC chips, which are in the moon rover camp: divide-by-zero is zero. Really! Go get a PowerPC Mac, do a divide-by-zero, and you just silently get zero. Solution #1 baked into the ISA. Not many people seem to have noticed, so it can't have caused too much trouble.
(Apologies for reposting my reddit comment here)