Finding "sub-palindromes".

J, 24 31 40

~.(#~(1<#*]-:|.)&>),<\\.

Sample use:

   ~.(#~(1<#*]-:|.)&>),<\\. '12131331'
┌───┬───┬───┬────┬──┐
│121│131│313│1331│33│
└───┴───┴───┴────┴──┘
   ~.(#~(1<#*]-:|.)&>),<\\. '3333'
┌──┬───┬────┐
│33│333│3333│
└──┴───┴────┘

Take that, GolfScript!

Python 124

r=raw_input()
l=range(len(r))
print', '.join(set('"'+r[i:j+1]+'"'for i in l for j in l if i<j and r[i:j+1]==r[i:j+1][::-1]))

Haskell 98, 88 91 96

import List
main=interact$show.filter(\x->length x>1&&x==reverse x).nub.(tails=<<).inits