For athletic and merit-based scholarships, the marriage should have no effect.
If a scholarship is need-based, the university or state or other organization that gave the scholarship may adjust the scholarship money up or down based on the new situation, taking the new spouse's finances (or lack thereof) into account. In particular, instead of looking primarily at the income of the student's parents, they might instead look only at the married couple's finances. But every scholarship is different they'll have to investigate the rules for the particular scholarship.
Being dropped from the parent's health insurance after getting married may happen, depending on the insurer's rules and the laws of the state.
Taxes will have to be filed as married*, which could result in more taxes being paid, although in most cases married-filing-jointly brings a tax reduction if one spouse earns much less than the other spouse.
*if they marry now, they would still file as single for the tax returns due in April of this year, since this April is the due date for 2011 tax returns, and they weren't married yet in 2011.