Generally, current tax law allows girlfriends(and boyfriend's too) to be a dependent on a tax return. Girlfriends are allowed dependent status as a "relative" if they have under $3,650(2009) in income and lived in your home for 12 months of the year. This is according to IRS publication 501.
There are rules that could eliminate your girlfriend from eligibility, like if they are still married or if their parents still claim them on a tax return, but in general it is possible to claim your girlfriend on your tax return.
Also this implied "relative" status allows your girlfriend's children to be included as dependents on your tax return in some cases. They must make under $3,650 and not be included on someone else's return.
Every situation is different so it is always best to get the blessing of an Enrolled Agent or CPA before you claim these exemptions on your tax return.
Now what is strange is that your girlfriend is allowed to be a dependent as a "relative" but she is not a "qualifying relative" for Head of Household. So you can claim her as a dependent but she does not allow you to claim the Head of Household status. And neither does her children.
If you have a girlfriend with a child it is possible that you could get the benifit of 2 extra exemptions on your tax return. Just make sure that your standard deduction status on the return stays "single".