Sums are not set as a test on Erasmus
Doc, note: I dissent. A fast never prevents a fatness. I diet on cod.
Yreka is the name of a town in NorCal. If you go there, you might look out for the
YREKA BAKERY
I’ve been there! Did you know the town has a mascot called Francis Fireweed? Tell you about it later.
Cain, am I maniac?
Go hang a salami, I’m a lasagna hog.
Sex at my gym taxes
Okay, but remember, you asked.
5’ G/AATTC 3’
Go hang a salami, I’m a lasagna hog – just the presence of the word lasagna makes this a winner. Who would think you could palindrome it!
A toyota’s a toyota - simple, yet so true. 
BTW, words that can be read upside down as well as right side up are not just palindromes, they are also known as ambigrams.
Nurse! I spy Gypsies! Run!
Call Ida, Collect Cello, Cadillac.
LOL, I have tears of laughter rolling down my face from the contributions here. Thanks, everyone. My biggest laugh in this thread yet:
My favorite Weird Alism:
LONELY TYLENOL
cmkeller, Aviva is such a lovely name in every way, it makes me wish I could have one more daughter, kayn ayin ha-ra! You were cool parents to choose that name. Hannah is my personal favorite because it’s etymologically the source of my name, my sister’s name, my mother’s name, and my maternal grandmother’s name. Really runs in the family. That it’s a palindrome too is just icing on the cake.
Said by Lou Reed when recording Metal Machine Music.
Do good? I? No! Evil anon I deliver. I maim nine more hero-men in Saginaw, sanitary sword a-tuck, Carol, I–lo!–rack, cut a drowsy rat in Aswan. I gas nine more hero-men in Miami. Reviled, I (Nona) live on. I do, O God!
Or its longer version:
Naomi, sex at noon taxes, I moan.
The on campus zipcode for my university is a palindrome. When I got my housing information for my freshman year, I immediately exclaimed, “My new zip code’s a palindrome!” My dad gave me a funny look; I can’t imagine why.
Alas, I am off-campus now. I have working heat, but a boring zip code.
-Mosquito
I read somewhere that aibohphobia means “fear of palindromes”.
That was my favorite, until I looked it up and discovered it wasn’t actually a word.
Do geese see god?
I believe we have a Doper whose name is a palindrome: I LOVE ME, VOL I
Lice? Cecil.
You gotta see this series of books by Jon Agee:
Be sure to use the “search inside” function on Amazon and see some of 'em. It’s the illustrations that make it!
Check his other titles.
Does “Today I’m talking in palindromes:|:semordnilap ni gniklat mi yadot” count?
If we can allow that, we’ll have to allow
A Fool, A Tool, A Pool; LOOPALOOTALOOFA!
I like:
A man, a plan, a cat, a canal - Panama! It surely says something about the universality, and adaptability, of cats that one can fit in there.
Top step’s pup’s pet spot.
A dog! A panic in a pagoda!
Lived on decaf, faced no devil.
Marge lets Norah see Sharon’s telegram.
Some men interpret nine memos.
Neil A. sees alien! Oh, so that’s why they had to fake the moon landing…
Cigar? Toss it in a can. It is so tragic.
Finally, the troubling litany of a hapless volunteer to the space program who is issued a red suit, a beard and (apparently) some very special sugar cubes…
A Santa at NASA.
A Santa deified at NASA.
A Santa dog lived as a devil god at NASA.
A Santa lived as a devil at NASA.
A Santa lives evil at NASA.
A Santa pets rats, as Pat taps a star step at NASA.
A Santa snaps pans at NASA.
A Santa snips pins at NASA.
A Santa spat taps at NASA.
A Santa spit taboo bat tips at NASA.
A Santa spits tips at NASA.
A Santa spots tops at NASA.
A Santa stops pots at NASA.
A Santa taps Pat at NASA.
A Santa’s rats top Nat, as Satan pots tars at NASA.
As I let animals laminate Lisa.
The Dover book Palidromes and Anagrams, edited by Howard W. Bergerson, has sone incredibly long ones, using unexpected words. A sampling:
Goddesses so pay a possessed dog.
Egad! Loretta has Adams as mad as a hatter. Old Age!
Lew, Otto has a hot towel.
Madame, not one man is selfless; I name not one, Madam.
Revenge my baby Meg? Never!
Pusillanimity obsesses Boy Tim in “All is Up”.
Too far away, no mere clay or royal ceremony, a war afoot.
Did I fish? Tim’s rod or Smith’s if I did.
Er…I fondle her as late petals are held – no fire.
No ostracised art for Eliot, a toiler of trades, I cart soon.
'Tis sent! I wed a mermaid – airy, mad, I’m amid a myriad, I am remade. Witness it!
Worse – Kama Sutra. Sad loss, sold as art. USA makes row.
Last fig as a gift, Sal.
“Pupils!” I say as I slip up.