Already in the case of finite symmetric groups, one can find any polynomial with non-negative integral coefficients and constant term 1 as KL polynomial for some pair of group elements.     See the paper by Patrick Polo <a href="http://www.ams.org/journals/ert/1999-003-04/S1088-4165-99-00074-6/S1088-4165-99-00074-6.pdf">*here*</a>.    But specific examples take a little more work.    Check the old tables for Weyl groups (and affine Weyl groups) on Mark Goresky's webpage at IAS <a href="http://www.math.ias.edu/~goresky/tables.html">*here*</a>.