Praveen, ikegami, Grandfather, etc all had wonderful ideas.

I'd use grep, but my code would probably look like this:

@array = (1, 0, 2, 0, 3, -1, 0, 4, 0, -5, 0, 123);
@nonzeros = grep {$_} @array;
[download]

or

@array = (1, 0, 2, 0, 3, -1, 0, 4, 0, -5, 0, 123);
@nonzeros = grep {$_ != 0} @array;
[download]

Both are based on the assumption that the array's contents are strictly numeric; if you want to remove strings, your grep would require a different regex.