Perl being big on "more than one way to do things...", semicolons are easy to discard:

  sub nextq {
      my $sz=8; 
      (print("@_\n"),return) if @_ == $sz;
      foreach my $col(0..$sz-1) {
          my $row;
          if (grep($_==$col,@_)) {next} else {$row=@_}
          if (grep($_==$col-$row--,@_)) {next} else {$row=@_}
          if (grep($_==$col+$row--,@_)) {next} else {$row=@_}
          nextq(@_,$col);
      }
  }   
  nextq();

I still feel that's cheating as you're just replacing the semi-colon with braced blocks; effectively it's still being parsed as multiple lines.

I was thinking more along the lines of using the one line conditional:

    condition ? first_expression : second_expression;

eg

    sub nextq {
        (print( "@_\n" ),return) if @_ == (my $size = 8);
        foreach my $col(0..$size-1) {
            my ($row, $next);
            grep ($_ == $col, @_) ? $next=1 : $row=@_;
            grep ($_ == $col-$row--, @_) ? $next=1 : $row=@_;
            grep ($_ == $col+$row--, @_) ? $next=1 : $row=@_;
            nextq(@_,$col) unless $next;
        }
    }   
    nextq();

The `$next` ugliness is due to not being allowed to use the `next` inside a one line conditional. There's probably cleaner ways of doing the above though. But that was only a quick hack.

It's almost as if "number of lines" isn't particularly meaningful.

I agree but we've already done that argument to death (eg the Plan 9 vs GNU debates about code "complexity")

This sort of line counting is just for fun.

Smaller without being obfuscated:

  sub nextq {
      my $sz=8;
      (print("@_\n"),return) if @_ == $sz;
      o: foreach my $col(0..$sz-1) {
          my($u,$d)=(scalar(@_),scalar(@_));
          for (@_) {next o if($_==$col or $_==$col-$u-- or $_==$col+$d--)}
          nextq(@_,$col);
      }
  }
  nextq();

Personally I'd consider 1 and 2 character variable names as a form of obfuscation. eg what's the point having a "pseudo-constant" for size if it's named in such a way that isn't immediately obvious that it refers to the size.

Nice code though.