I am not certain there are "must play" courses but there certainly are "must play" kinds of courses. They would include: 1. links golf. Golf began on the coasts and to understand its roots we need to start there. 2. Heathland golf. When it moved inland, it moved to these wonderful courses. The heathland courses in England are not replicated anywhere else. 3. Top 100 courses. It is important to have played some of the greats so one can compare better. You need to see what works. One could not do much better than to play Shinnecock, NGLA, and Sebonack. Three different courses on similar terrain. 4. Dog tracks. You need to see what doesn't work. 5. A variety of courses: eg. desert courses, parkland courses, Florida courses, mountain courses. 6. Play a variety of different designers: Old Tom (where you can find one that hasn't been to drastically altered), Colt, Mackenzie, Ross, RTJ, Wilson, Dye, etc.
If you have not seen a variety of course in a variety of places, by a variety of designers, how can you speak knowledgeably?