As of 2012, you must have provided at least half the support for any dependent. Additionally, for the tax year involved, the dependent must have lived with you for at least six months plus one day. A dependent must be your son, daughter, granddaughter, stepchild, foster child or a descendant of one of these persons, under the age of 19 at the end of the tax year (or 24 if a full-time student) and who must not have filed a joint return.
Your 17-year-old may qualify as a dependent, but not for some additional tax credits. For instance, in order to qualify for the Child Tax Credit, a dependent must have been under the age of 17 at the end of the tax year.
Only one tax return can claim an exemption for a dependent per tax year. If you and someone else both qualify to claim a dependent, use the tie-breaker rule outlined in IRS Publication 501 to make a final determination as to who has the right to claim the dependent.