There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.
Turning 24 only means you can no longer be a Qualifying Child dependent. But, you may be a Qualifying Relative dependent. As others have said, this can only be if your parents provide more than half your support and your gross income is less than $4400.
