Guilty of skimming the responses, but nowhere did I see mention of Royal St. George's which must surely be part of the conversation. I might have played it on a particularly tough day, but I found it harder than Carnoustie. And I think I must have visited the European on a day when every hole was playing downwind because I didn't find it as challenging as some folk here. Great course no doubt, but not unduly difficult.
My top five would be:
1. Royal St. George's
2. Carnoustie
3. Royal Portrush
4. Royal Liverpool
5. Royal Birkdale
(also think Trump's course at Aberdeen is worth considering, but the rough may now be a little less ridiculous than when I played it
in 2012.)