Hey, check this out--Lorne Rubenstein wrote an article about this very topic and theorized with Tom Fazio about it!
http://services.golfweb.com/library/lorne/lorne961016.html He knew of only two palindromes: TOC and Weston G&CC, a Willie Park design in Toronto. He also mentions the two palindrome nines at ANGC. Out of 188 courses in the World Atlas of Golf, only TOC was a palindrome and only 5 had palindromes for a single nine holes.
Interesting article! It's fairly long, but here's a portion:
"Only the Old Course had a complete palindrome right through the card. Evidently, this is extremely rare. I did find one other 18-hole palindrome, and in my own backyard. The Weston Golf and Country Club in Toronto is an old and classy Willie Park design; Arnold Palmer won the 1955 Canadian Open there, his first win as a professional. And the scorecard at Weston reads the same back to front. Perhaps you can find a complete palindrome in your own area.
When I first discovered golfing palindromes, I called noted architect Tom Fazio. I wondered if there was something hidden in palindromic courses. After all, Augusta National and the Old Course are two of the most celebrated courses in the game. And golf connoisseurs in my neck of the woods like to get out to Weston whenever they can.
Could it be that palindromic courses have an integrity, an internal consistency, that other tracks lack?
"My first reaction is that it's just a chance happening," Fazio told me. "If anybody asked me to design a course with that numerical sequence, I don't think I could do it. Other considerations would be more important."
Fazio and I had a pleasant, rambling chat. It was easy to see that his interest had been piqued and that he would be giving more thought to the matter of golfing palindromes. Soon he warmed to the subject.
"I wouldn't mind checking it out to see if there's some phenomenon related to the sequence that works on a mystical plane," Fazio said, now thoroughly warmed to the unusual sequences on but a few courses. "And I'll tell you, you could do it on flat terrain, where you in effect create your own topography by moving earth. It could have been done at Shadow Creek (the lavish course in Las Vegas that Fazio designed for owner Steve Wynn), where we created something from nothing." "
BTW,
I have checked all of the courses I have played and other scorecards I have collected (over 400 courses), and I've only found 1--TOC.
So the count so far is 3: TOC, Cowansville GC in Montreal, and Weston G&CC in Toronto.
Any in the U.S.?