I believe a lot of people, much like myself, approach your question from their own state rules and regulations. Each state is different on how they classify "girlfriend".
I live in California, so, I will answer it this way. It is fairly simple to get added to your boyfriends plan with a notarized affadavit of domestic partnership. From that point in time, you have less than 30 days to get on your boyfriends plan. It would be the same as if you were to get married, or he had a child (natural or adopted)...because there is a change in his "family" structure from single no dependents to "domestic partner" this legally allows the company to add you.
Now, this being said, the company that he works for does not have to pay for any amount of your health insurance premiums. They just have to allow you to join the plan.
The only caveat to this is if your boyfriend works for a large enough company where his company's insurance is out of state. Then it gets more complicated. The easiest way to resolve is for YOU to call his benefits department and ask them about domestic partnerships and...how much it will cost.
Hope this helps...take care,