First question is, where exactly are you located, you’ve lived in different parts of the world and in fact, marriage will be recognized in all countries but partnerships will be viewed differently as soundedfury has already pointed out.
Not just from the point of the rights of the partner, but also of the children, the father will have to sign paternity affidavits for the children, for example.
Socially it’s hard to say, and largely dependent upon where you make your home, right down to the neighborhood. If you, for example, move to a somewhat conservative neighborhood you may find that your children may not be entirely accepted. Your child may have problems at schools, and I’m speaking from experience. I think we’d like to believe that we’re advanced enough to deal with this issue without discrimination, but there are places and people where discrimination based on your situation may exist. You will undoubtedly be asked why you just don’t marry.
Even though I don’t have an issue, there are some who do. It’s the reality.