Fun courses involve a lot factors, probably too many to mention.  For me an ideal fun course is mainly about balance.  

The course should offer some difficult (including a few do or die shots), easy and funky drives, approaches and greens (varying in size as well).  A few blind shots are essential.  Plenty of doglegs of varying degrees.

3-4 par 4/5s which are driveable/reachable.  No par 3s (I would like at least 5 par 3s) which require a wood (well, maybe one if it is a great par 3).  At least one par 4 (maybe two) that is terribly long, perhaps playing just as long as a reachable par 5.

The land should be rolling (uneven lies are a must) or have some elevation (maybe a few sharp falloff areas), something which eliminates the need for loads of bunkers (some bunkers should be blind and I prefer smallish bunkers that are discrete though a few biguns to liven things up is great).  A few burns would be excellent.  Very little serious rough in play.  Wide fairways, maybe 50-60 yards wide, but there should be some variation.  A few narrowish fairways are fine.  Some centerline features (humps are excellent) from the tee and approaching.  

A lovely setting is essential.  The course should be maybe 6500 yards or whatever length that makes distance a non-issue.  I don't want to think that I need to play smash mouth golf to get around.  The conditions should be f&f, but not so as to take the driver out of the players' hands.

There are other things, but it is sometimes difficult to pinpoint what is fun about a course.  

Ciao

Sean

Rich

If a guy is gonna dream he may as well dream big!

Ciao

Sean

Jeff,
I think it's mostly about success, it's the most widespread measure of fun. Players from any era would/will feel good about a course that offers them challenge along with opportunity. It's not just about scoring well, although I think that's important, much of the fun depends on how you as an architect choose the elements and blend them all together. Players aren't the wussies we sometimes think they are, they will accept tests as long as they're provided with some ways to deal with them.
So I say, be as bold as the guy with the money allows you to be. Mix up the shots and throw in the occasional unkempt, cavernous bunker. Hazards aren't a problem if you're not in them so leave a way around and you'll make it fun for most everyone.  

Bold hazards (natural and man-made), challenging greens and variety.

The sad part is that there seem to be a lot of golf architects who have never even asked themselves this question.

I find myself in agreement with nearly all of Sean's answer.  I don't know that "a few blind shots are essential", one or two serve amply for me at Crystal Downs, Pacific Dunes, Cypress Point, Muirfield, Dornoch, Merion, and other favorites.

Jeff:  What "shuts down the offense" in your analogy are fairways that are too narrow, rough too penal, too many trees or water off the tee.  Rolling greens are the element that allow you a lot of chances but limit the number of goals.

A few thoughts are variety, creativity, cleverness, whimsy, quirk, having finsihed with a sense of accomplishment, not losing a lot of balls in the woods, water or gunch, big, fun curving roller-coaster putts that give a smile to you when you just get near the hole.

 Tee shots that end up in play. The lost ball or penalty stroke comes from me taking on too much risk , not just missing a shot. Second shots on par fives that have choices. Approach shots to par fours that use numerous clubs and several types of shots. Variety of shots to par threes. Challenging putting from mishits or mistaken strategy.

  Not punching out from trees more than once or twice; not watching a ball bounce from the fairway into parallel water ; not hitting a good shot on a blind hole and finding yourself in a hazard.

  All done while walking with friends.

"Fun" courses have:

(1) Strategic design--generally, a course should be big enough, with large enough greens to offer different playing challenges every time you play it.

(2) Options--safe and risk/reward routes to the holes should be  present on several holes.

(3) Demanding Shotmaking--an examination of the entire bag of 14 clubs always makes you hit a few shots imperfectly enough to make you want to try them again.

(4) Beauty/Conditioning--I've never enjoyed a round on an ugly or poorly conditioned course.

(5) Good pace of play--long waits between shots limit enjoyment, no matter what #s 1-4 are.

In my Southern California Sampler thread, I thought Rustic and Stone Eagle were very fun, Bighorn Mountain was fun and Angeles National was like going to the dentist.  Perhaps you are being justly punished, but who wants that?

1.  I think for most people, fun to play, means in the first instance, avoiding the need to search for lost balls.  

2.  Agressive play is fun.  Defensive play is not.

3.  Thrilling carries on an aggressive line are fun, even if they are not that challenging.  From the members tees, Royal Melbourne has a bunch of bunkers that can be easily carried with a decent tee shot.  

4.  Short par threes are fun for everyone.

5.  Some mystery associated with slopes near the green that can be used to one's advantage.

6.  Reachable par fives and par fours are fun.

7.  Variety in approach shot length and difficulty.

8.  I think for most people playing a CCFAD or a public course for the first time, predictability is fun.  In other words, if one is chopping it around and then hits a career shot, they want a good result and are sorely disappointed if it does not happen.  Frustration sets in quickly if that does not happen.

9.  Fast conditions are fun.  Everyone likes to think they hit it farther than they do and the thrill of having a driver take a big hop forward provides a thrill and rewards accuracy.

10.  Wide fairways still should be interesting due to better lies or better angles into the green.  I disagree with Jack Nicklaus' second shot course concept to the extent that if a course is wide and featureless, it becomes boring if I am hitting it well off the tee.

11.  Decision-making is fun.

12.  Slow play and poor conditions are probably the factors that contribute most to dissatisfaction with a course.

13.  Courses that can be walked easily and quickly are fun.

14.  Something that makes you chuckle is fun - either a good bounce, use of an existing barn on a course or the occassional bunker that might never be in play but is there for no good reason are good reminders that you are playing a game.

15.  A course that allows you to shoot a good score when playing well is fun.    

A couple of things to add to all the above excellent responses:

1.   Risk / reward shots that can be achieved by an average golfer hitting a solid shot from the appropriate tees on the perfect line.  That's "fun."

2.   The joy of watching the ball take the right contour on the green and slowly roll toward the pin, even if the right contour is 100' to the other side of the green.  That's really "fun."

In general, having options on every shot.  Has anyone here played Jacaranda in Plantation, Florida?  I was thinking of that course yesterday during the "centerline bunker" thread.  No centerline bunkers at Jacaranda, but literally every par 4 or par 5 has two fairway bunkers on each side of the fairway about the same distance from the middle tees so the only playable line is down the middle.  And bunkers front left and front right of every green.   That's the exact opposite of "fun" golf.

For me it begins with anticipation, the desire to play the course. For example, how many on here have gone to Scotland, Ireland, Australia, etc,,, to play and have been anticipating stepping onto TOC, Royal Melbourne, etc... for the very first time?

Isn't the excitement of anticioation part of the fun? And isn't it that way every time you walk onto a course, even if you've played it many times before, because you enjoyed the "hype" of the anticipation you gave yourself.

It's that way for me at Bethpage Black. I've played it hundreds of times yet the fun of walking those fairways are always there for me.

The ooposite happens when we anticipate an experience that doesn't happen. Again, for me that was Pinehurst #2. With each hole played, the hype and what I believed I should be experiencing weren't happening. So I have no desire to play it again.

Fun is relative and personal as is anticipation.

Windmills that actually spin and block the entrance to the open area underneath, skinny bridges to putt over, metal 360* loops, Clown's mouthes, several holes with different outlets all make miniature golf fun.

There is one in Mystic Ct that has all of this that one can play before or after Fenwick Island 9-holer.