My UK GF is pregnant with my child

As you can tell from the title, my UK citizen GF is pregnant with my U.S. fathered child.
Do I have any rights, ways or means to join my soon to be family in the UK? I can not even remotely dream of a life without the both of them in it. The only hindrance has been immigration laws.

You can make plans to marry the mother of your child and would have no problem getting a fiancé or spousal visa (assuming you have funds to support yourself and no criminal convictions etc). 

Can you get married and can you support yourselves with savings/income? Get married and get a spousal visa, and then you can move to the UK.

If you are asking if you will be granted rights to live in the UK simply b/c you have fathered a child by a UK citizen, the answer is no. 

As the others have said, you will need to marry the mother of the child and prove the two of you can support your family without access to any additional public funds for YOU  in order to be able to live and work in the UK. (unless you qualify for a work based visa or plan on going back to school)

There is the 'access to child' visa that you can apply for from the US. However, the child would have to be born and you would need a court order for contact/visitation or joint custody. This would only be an option if your relationship with your GF broke down and it was your only option to see your child.