I don't know any good palindromes but I enjoyed "I Palindrome I" by They Might Be Giants. Very clever song with palindromes as a theme. Palindromes in many different forms.
Someday Mother will die and I'll get the money
Mom leans down and says, "My sentiments exactly
You son of a bitch"
I palindrome I (I palindrome I)
I palindrome I (I palindrome I)
And I am a snake head eating (snake head)
The head on the opposite side (snake head)
I palindrome I (manonam)
I palindrome I (manonam)
See that bulletproof dress hanging from the clothesline
See the medical chart with the random zig-zag
Now I'll help it decide
I palindrome I (I palindrome I)
I palindrome I (I palindrome I)
And I am a snake head eating (snake head)
The head on the opposite side (snake head)
I palindrome I (manonam)
I palindrome I (manonam)
I palindrome I (manonam)
I palindrome I (manonam)
"Son, I am able," she said
"Though you scare me." "Watch"
Said I. "Beloved," I said
"Watch me scare you, though"
Said she, "Able am I, Son"
See the spring of the grandfather clock unwinding
(Egad, a base tone denotes a bad age)
See the hands of my offspring making windmills
(Egad, a base tone denotes a bad age)
Dad palindrome Dad
I palindrome I (I palindrome I)
I palindrome I (I palindrome I)
And I am a snake head eating (snake head)
The head on the opposite side (snake head)
I palindrome I (manonam)
I palindrome I (manonam)
I palindrome I (manonam)
I palindrome I (manonam)