Recreating this experiment to confirm universal gravitation would be awesome. Construction of the experimental apparatus should be well within an intelligent 8-year-old's abilities - all you need to provide/acquire is the idea and the more specialized equipment (e.g. lead weights). You can go shopping together for the more common stuff (nylon monofilament, etc.).
Finding a suitable location is probably the trickiest part, but the reward would be well worth it - this is a real scientific experiment, the Cavendish experiment, which wasn't carried out until after Newton's lifetime. It is also something that nobody ever does in school, because our schools are lame and boring.
Fourmilab's version is bogus... given the masses involved, a calculation using f = GmM/r^2 shows that it should take a lot longer for the moving mass to reach the test mass than it does in the video. The most likely explanations for what is seen in Fourmilab's video are static electricity or outright fraud. (Incidentally, my father actually did build a working Cavendish experiment in our basement; it uses much larger fixed masses and a thinner wire, and it does indeed move much more slowly. It turned out to be very difficult to get it to work; the effects ...
I have an 8-year-old sister who is very interested in science. The school she attends (in rural Indiana) takes the mantra of "teaching to the test" to a whole new level; my sister has already come home from school many days crying and stressed over fear that she won't pass her state's proficiency tests (which are 5+ months away). They are underfunded and the science curriculum is what most of the (overtly religious) teachers are undertrained in, and so science is essentially not addressed. My sister has about an order of magnitude more homework on cursive writing than on anything related to science.
I want to purchase a gift for her for the holidays this year (the occasion doesn't matter, but it's a time when I'll actually be home so I can give her the gift and play with her / explain how to use it / hopefully help her start thinking about some things). I'm willing to consider age-appropriate ideas across several price ranges, but I want to think of something that will deliver a lot of utility: i.e. it should be compelling enough that an 8-year-old will actually like using it and there should be at least some evidence that she will benefit from it.
I've considered things like the EDUbuntu computers that come with lots of educational software, but actually buying one seems to be not straightforward. Is the best thing to buy a cheap netbook at then install EDUbuntu myself? Is a netbook too much for an 8-year-old? I'm mostly focused on things that will help her be proficient with computers and potentially help her develop a more sophisticated interest in them as she grows up. The Lego Mindstorm robotics stuff also crossed my mind.
Does anyone have experience with this / know of resources for making a good investment? Or am I way over-thinking this and just some regular Legos or art supplies are going to do essentially just as much good?
Added 02/25/2012
Much of the advice was very helpful. I ultimately found out that my young sister was interested in "mixing chemicals together because it looked cool." An item that I found which looked like a good way to bridge the gap between her more girly interests and her interest in chemistry was Perfume Science from Thames and Kosmos. I also purchased a variety kit from Snap Circuits. She loved both items and we spent a good bit of time playing with them during my trip home to see my family. We made several different kinds of perfume and also did some activities that helped explain how different extracts have been acquired throughout human history for their smells. Ultimately, my sister made a science fair project (something which surprised my parents a lot) based around one of the activities in the perfume science booklet, and she won second place.
I was very happy with both my decision to ask this question on LessWrong (despite the title of the post, which seems to seethingly annoy many LWers) and my purchase decisions. I used the website Fat Brain Toys to purchase the items and everything arrived without a problem. That site seemed to also have a reasonably good selection for more educationally oriented toys across several ages, and with useful customer reviews.