Applying same graduation school with my girlfriend, is it ethical? Me and my girlfriend are currently studying in the same university and same department. We both applied couple of master's degree programs abroad. 

One of the programs is in both our interest and she already got accepted for that program. I want to apply for the same program too but there is no question regarding your spouse / girlfriend etc. Should I notify the program about this in my application?
At best, that information would be (should be) irrelevant to them. You want to be accepted on your own merits in any case and a fair evaluation will, hopefully, assure that. 

But you also need to be flexible in planning your own future. For example, if there are other universities nearby, it would be good to also make application there. Then, if you don't get accepted into the same place, your relationship can still survive. 

But a relationship can, if strong, still survive a couple of years of separation. 

But give it your best shot. Riding someone else's coattails isn't a strong point in your favor and people are unlikely to change relative rankings of candidates for such reasons. 

And yes, it is ethical to apply to the same programs, if that is your real concern. 



Let me give you a worst case scenario, though it would be unethical and I doubt that any university would follow it. But suppose you tell them and they decide not to accept you and think that she, then, won't come either. They then rescind her offer and offer it to someone else. Some programs, notably in medicine, need to fill every slot since it is expensive to run a program partially populated. 

I seriously doubt this could happen, but I recommend against inserting wild cards into the decision process.