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 and student status test, a relationship test and a residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. The Other dependent (qualifying relative) credit is worth (up to) $500 per dependent and is non-refundable. That is, it can only be used to reduce an actual tax liability.
In addition to the above requirements, to claim your girlfriend's children, they must meet all of the above requirements and:
--- your girlfriend must not be required to file a return,
--- she does not file a return claiming the children
As others have said, legal step children are the same as biological children. After you marry, her children will meet the relationship test and you can claim them as Qualifying Children, whether you file a joint or separate tax return.
