Examples of how can it bite you I could find were really simple. Classic 'newline after return' doesn't go away if you put in semicolons manually because it happens because even if you put them in manually they are still inserted in other places you didn't expect and you have to be still aware of that.

The other bug I've seen is when you start a line with '(' which will be interpreted as function call of a function from previous line. Putting in semicolons at the end of each line saves you from that almost always easily detectable error. But you'd be just as safe if you just put ';(' at the begining of next line instead of '('. And I think starting a statement with '(' is weird enough and specific to javascript (in C family) that ';(' is not much weirder.

I use semicolons in js but for purely esthetic reasons so it looks like Java, C++, PHP, C# and such.