for(my $x = 0; $x <= $#array; $x++) {
    next unless $array[$x];
    # do stuff with $x and $array[$x]
}
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But that is obviously inefficient, especially if your list is VERY sparse. Like with elements numbered 100, 435, 1040, etc.

Why not use a hash? You can convert a sparse list to a hash like so:

my %hash = 
    map { $x => $y } 
    grep { my $y = $list[$x]; $y ne $undef; [$x, $y] }
    for(my $x = 0; $x <= $#list; $x++);
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And use it like this:

$list{100} = 'dog';
$list{435} = 'cat';
$list{1040} = 'tax form';

while(($index, $element) = each %list) {
    # do stuff with $index and $element
}
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Other alternatives include using a pseudohash, or writing a tied array implementation that acts like a list in your code but works like a hash behind the scenes.

Instead of the map/grep/for mess I gave you, try something like this to convert a sparse list to a hash:

my %hash = ();
for(my $x = 0; $x <= $#sparse_list; $x++) {
    my $y = $spase_list[$x];
    next if $y eq undef;
    $hash{$x} = $y;
}
[download]

As an aside, you can use exists and delete on array elements but it comes highly discouraged. So don't do it.

Apologies for the typos...

The problem is that I need fast *ordered* access, something that a hash really won't help me with.