Short answer is stone, even though I build marble wonders much more frequently than stone wonders.
Marble wonders tend to be more generalist: Oracle, Great Library, national/heroic epic, Taj Mahal. They're useful if you get them, doesn't matter if you don't, and doesn't define a strategy. I don't build all of the above, but I do end up building at least one.
Stone wonders are expensive, and more niche, but also more potentially game-breaking or game-changing. Unfortunately, because they are game-changing, the AI will often complete them first with their bonuses. If I happen to have stone, I would definitely build one of those wonders and shape my strategy for one of those amazing world wonders.
Is it also a co-incidence that many of the voted 7 wonders on 07/07/07 are stone wonders? I think not. Stone as an architectural material has a unique feeling that nothing else could reproduce.
The Great Wall is a great example, but for a different reason. I don't shun from barbarian activity at high levels, because I see them as "free exp", with the notable exception of the stupid stack-of-archer event. Also, a great spy at higher levels means you can steal tech and really come back.