separation

What is the name of your state? Pennsylvania

I have lived with now my ex-girlfriend for about 10 yrs.
We bought a house in 2000 and separated in 2002. The house
is both on our name. When we separated last October 2002, I
moved to a different state. She's been paying for the mortgage since I left. I just want to know what I am entitled to the property. In other words, I want my name out of the house and get my share of the property a soon as possible. What should I do?

Your name will not be removed from the mortgage until it is refinanced in her name alone. Hope she is able to do that and buy you out. You may also take her to court to force a sale of the house.

Thank you for the advice!
If she desides to sell the house, am I entitled to 50%
of the equity/value of the house? If not, what am I
entitled to?

Rightfully, some or all of the mortgage payments could be considered rent. She will argue all the appreciation since you moved out should be hers. You will counter by saying she owes you some interest on your investment from the date you moved out.
Of course, you should get back your initial investment plus half of appreciation to the time you left. Anything more is open to negotiation and what is equitable. (Equity means no one is happy.) Perhaps a mediator can help you resolve this at a minimal cost. Once you get involved in a suit only the lawyers win.