Omitting leading whitespace this is 97 chars:

sub nn_single {
    @_=sort{$a<=>$b}@_;
    $_{abs$_[$_]-$_[$_-1]}=[$_-1,$_]for 1..$#_;
    @_[@{$_{(sort{$a<=>$b}keys%_)[0]}}]
}
[download]

I worked on this without looking at your solutions but it is very similar to your nn3. Great minds?
If the list contains duplicates then the following will work. Omitting leading whitespace this is 114 chars.

sub nn_dup {
    my$s=sub{sort{$a<=>$b}keys%_};
    @_{@_}=0;
    @_=&$s;
    %_=();
    $_{abs$_[$_]-$_[$_-1]}=[$_-1,$_]for 1..$#_;
    @_[@{$_{(&$s)[0]}}]
}
[download]

Update: I've updated this for a numerical sort and included snowcrash's %_ hack. danger, as usual, looks like the one to beat.

John.
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