Palindromes are words or phrases that read the same in both directions, e.g. EYE,or RACECAR, or MADAM I'M ADAM. Here are a few good ones:

Don't nod
Dogma: I am God
Never odd or even
Too bad – I hid a boot
Rats live on no evil star
No trace; not one carton
Was it Eliot's toilet I saw?
Murder for a jar of red rum
May a moody baby doom a yam?
Go hang a salami; I'm a lasagna hog!
Satan, oscillate my metallic sonatas!
A Toyota! Race fast... safe car: a Toyota
Straw? No, too stupid a fad; I put soot on warts
Are we not drawn onward, we few, drawn onward to new era?
Doc Note: I dissent. A fast never prevents a fatness. I diet on cod
No, it never propagates if I set a gap or prevention
Anne, I vote more cars race Rome to Vienna
Sums are not set as a test on Erasmus
Kay, a red nude, peeped under a yak
Some men interpret nine memos
Campus Motto: Bottoms up, Mac
Go deliver a dare, vile dog!
Madam, in Eden I'm Adam
Oozy rat in a sanitary zoo
Ah, Satan sees Natasha
Lisa Bonet ate no basil
Do geese see God?
God saw I was dog
Dennis sinned 

2D Palindrome Squares

In these word squares, a word can be read in either direction in every row and column. Here is a selection of 3x3, 4x4, 5x5, and 6x6 palindrome squares in English.