Palindromic numbers are not uncommon -- recently (in the July 12 posting) power-of-eleven palindromes are mentioned. Palindromic poems are more difficult to find but see, for example, the postings for October 6, 2010 and October 11, 2010.
At a recent Kensington Row Bookshop poetry reading, Hailey Leithauser revealed that all but one of the poems in her recent collection Swoop (Graywolf Press, 2014) contain a palindrome.
And here are a couple of my favorite palindromic phrases:
(the impossible integer)
Never
odd or
even.
odd or
even.
(the mathematician's answer when she is offered cake)
"I prefer pi."
"I prefer pi."