I came up with this recursive-regex code. It's a bit simpler than most of the others posted here. It finds the leftmost longest palindrome in each line.

my $palin_re;
$palin_re = qr/(([a-z])    # First letter
               [^a-z]*     # any irrelevant chars
               (?:(??{$palin_re})|[a-z]?)  # The interior  
               [^a-z]*     # any other irrelevant chars
               \2)         # the last letter matches the first
             /xi;


while (<DATA>) {
  if (/\b$palin_re\b/) {
    print "Matched $1\n";
  }
  else {
    print "No palindrome found in '$_'\n";
  }
}

__DATA__
oo
madam in eden, I'm Adam, prince of eternia
is god a dog?
nested testest detsen nested
i prefer pi ip referp
nothing to see here, folks.
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