My spouse and 2 kids have high deductible insurance, but I do not. If my spouse contributes to an HSA, could that money be used for my medical expenses, or only for expenses for the rest of the family?
If you file your taxes jointly, she can pay for you.
The money can be spent on any taxable dependent can for qualified expenses. The rules for how much money can be contributed to the account are based off of the number enrolled.
Since your spouse has your children enrolled, she can contribute the higher family limit (current $6250 in 2012) but that has no bearing on how she spends the money so long as the expense is a qualified one.
She could not pay for a cousin's expenses if that cousin is not listed on her taxes.
Because your wife has the HSA, you are not allowed to contribute to an FSA, so be careful with whatever insure you being provided by the university.