At the risk of sounding self-serving and elitist, I think the best intellectual training is mathematics and physics. These subjects are the most challenging to learn due to their abstract nature and extremely difficult to pick up as an adult (maybe as difficult as learning a musical instrument or foreign language as an adult). There are many claims that mathematicians and theoretical physicists make their biggest discoveries before the age of 40. Mathematicians and physicists have a reputation for being "smart" and after a long period of reluctance and doubt, I have to agree that this reputation is well-deserved.
If you know math and physics, it's easy to pick up almost everything else. I'm not saying you'll achieve a deep understanding of literature, history, or business, but you'll be able to learn it pretty fast and be decent at it. My friend remarked that the coolest people are the scientists who are the top in their field and interested in everything. Unfortunately, these people are a minority. The rest are rather one-dimensional and dull company. (Her opinion, not mine.)
I think that the other difficult fields to pick up are visual art and music. They are also quite abstract. Artists are trained to "see" in a special way; they can translate what they see into an artistic representation (often translating 3D into 2D). By visual art, I'm talking about drawing and painting, not photography (which is kind of a technological cheat). Musicians innately understand rhythm and scales.
I've heard that philosophy is the best intellectual training if you restrict yourself to humanities fields. I'm not really sure about social science. Those are interesting subjects, but I think if you just want to be a great thinker, you're better off starting with math and physics.
So I guess if I had a child, I would have him/her learn art, music, math, and physics, plus a couple foreign languages.