The hook
Not one wall but many, built and rebuilt over two thousand years and running for thousands of kilometres across mountains and desert, best met on a steep, half-wild section with a watchtower and no crowd.
01Why it's worth it
The Great Wall is less a single structure than a vast, patched-together system of fortifications that successive dynasties threw up along China's northern frontier over more than two millennia, the grandest surviving stretches built by the Ming in stone and brick. Contrary to the old story, you cannot see it from space with the naked eye, but on the ground the scale is still staggering: the wall rides the very spine of the mountains, dipping and climbing with the ridgeline, punctuated by watchtowers, for as far as you can see in either direction. Where you go matters enormously. The nearest restored section to Beijing, Badaling, is heavily rebuilt and mobbed; sections like Mutianyu are handsome and manageable, while wilder, partly-crumbled stretches like Jinshanling or Jiankou reward a hike with solitude and a truer sense of the thing.
02How to experience it
Skip Badaling for a better section: Mutianyu for an easier restored walk, or Jinshanling for a longer, half-ruined ridge hike with far fewer people. Start at opening or camp near a wild stretch for dawn. Wear real shoes; the steps are steep, uneven, and endless.
The honest note
The most-upvoted advice in the r/travel China thread is an argument against spending your trip on the famous sights: "my best advice is to get out of the cities as soon as possible. Many tours are Beijing–Xi'an–Shanghai–Chengdu. The cities are great, but in the end not that different from those in the rest of the world. By far the most interesting stuff lies in-between."
It did not go unchallenged, and the rebuttal is worth as much as the claim: "I can't help but say he is absolutely wrong — if you have never been to China, going that route would be the best. There is a wealth of cultural history dating back thousands of years in those cities." Both are experienced travellers, and the disagreement is the useful part: the Wall and the Terracotta Army are extraordinary and they are the itinerary everyone already has.
One practical note that has outlasted the thread: the Great Firewall. "Almost all of the large western websites are blocked, so don't expect anything related to Google or Facebook or Twitter to work." Plan your maps, mail and messaging before you fly rather than after you land.