Just off the top of my head:

1.) ($concat = $a) .= $b;
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perhaps more will follow. (and they did....)

2.) $" = $b; @_ = ($a,undef); $concat = "@_";
3.) do { $concat .= $_ for (split(//))} for ($a,$b);
4.) my %a = ($a => $b); $concat = join'',each %a;
5.) $concat =~ s//$a/; $concat =~ s/$/$b/;
6.) $concat = <<"EOF"; chomp($concat);
    $a$b
    EOF
7.) $concat = `echo -n "$a$b"`;  # for safe values of $a and $b
8.) $concat = glob("{$a}{$b}");  # not Taint safe... will choke on met
+achars...
9.) ($concat) = ("$a$b" =~ /(.*)/);

And finally, everyones favorite Perl6 construct...
10.) $concat = $a _ $b;
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Update: Ok, now I get it... you want us to pick a simple operation and try to find $MAX+1 ways to do it, not necessarily just find other ways to do a concat. In that case, I'll set the original $MAX rather high by pointing at Adding 2 + 2, which ties perl-based-dynamic-webpage-templating-systems for the most most "ways to do it."

Update2: Added a few more to the list...

-Blake