If you're currently covered under your parents plan (or your kids are covered under your plan), look into staying there.  Under Federal law most health plans issued or renewed after September 23, 2010 must cover dependents until they turn 26.  This age limit applies regardless if the dependent is married, living at home, or out of school. 

If you've found a job with benefits and only need to wait short time for your employer's plan to begin you could apply for a short term medical plan.  As the name implies, these plans are designed to cover short time frames from one to six months after which time they will expire. 

Buy your own individual plan.  If you qualify you could apply for your own individual medical plan from a reputable carrier.  In many cases a good plan for a younger person can be found for less than $100 per month.  Contrary to what many people believe, the carrier just can't kick you off later if you get sick.  This is a more permanent solution unless you later move out of your carrier's service area. 

COBRA:  Under the federal law loss of dependent status is a qualifying event for up to 36 months continuation.  As stated above, graduating from school or getting married is probably not a qualifying event in itself. If you lose dependent status under your plan you can investigate your COBRA options. 

If you're on a student plan from school that will terminate, or you're not covered by your parents policy, and you can't qualify for an individual plan, you can check out your states high risk pool.  In Colorado that is CoverColorado or GettingUsCovered.