Great question, and one for the ages.....
I suppose you'll get answers ranging from Co-Ed naked golfing and flirting with cart girls to drinking beer in the clubhouse, but I'll confine my answers to what makes courses fun.
As an architecture buff, I always enjoy playing historic courses, like St. Andrews,
As an average golfer, I like scenic beauty. One thing I really like is walking down a narrow path from a green to the next tee and then having the hole "open up" to me as I come out of the opening, like coming up the ramp to a football stadium.
I like a feeling of enclosure, such as valley fairways like those in Ireland and Cruden Bay.
As a golfer who doesn't hit ground ball tee shots, I like carry bunkers, like San Fransico CC and Royal Melbourne - with todays clubs, its not a chore to fly them, but its fun to see the ball dissapear over them anyway. If I was really, really, sweating the carry, it would not be quite as fun.
I was thrilled with the tee shots at Castle Harbor and Mid Ocean, where the cross slopes and fast fairways really made you hit a tee shot to the high side of the fairway just to stay on the fairway. It was the first time I saw "save" bunkers that I felt were truly necessary.
I like "misdirection" approach shots, like Redans, or any other approach with a ricchocet bank (like 4 at Riviera) where you don't play directly at the pin to get where you want to be. At Sand Hills this year, I hit the first two greens, and on neither of them did my ball first land on the putting surface.
I like putting through Biaritz and Valley of Sin swales, but not to the extent that I would aim for them, a la Tommy N. at Pine Valley's Devils Asshole bunker!
I recall my first round in Scotland, where the wind had me playing 9 irons from 210 and 3 irons from 140, courses and conditions where the yardage book don't matter. In those cases, I love playing with a crusty old Scottish caddy who insults me all the way around. (Ya moved everthan but your bowels on tha swing, laddie)
I never play competitively, and if I did, I will be the first to admit that my list would be different.