In an expanding universe, what doesn't expand?
Richard Price has an article up on the arXiv that seems pretty relevant to some earlier discussion on my blog. He looks at the question of what happens to ordinary matter as the universe expands - what the effect is on bound systems like atoms, galaxies, and humans - and answers it at the level of undergraduate physics. Might be worth reading even if you don't dig the full-on math. (The short answer: If it is tightly bound enough, there are some transient effects but ultimately the expansion leaves the system unaffected. If not, it expands at the same rate of expansion as the overall universe. 'Tightly bound' means that the forces keeping the system together are strong)

It is reassuring, given the bit of floundering I did faced with this question, that such a brilliant physicist needed to think seriously in order to answer it :)