I can only think it's a legality thing when it comes to your inheritance from the will. It makes it clean.
Does does the marriage really make a difference in a will [serious]. You don't need to be married to set aside funds for someone, right? How do gay people do it in states where gay marriage isn't legal?
Stadler, get in here.
Marriage absolutely matters in an estate situation. A will can override that, and specific beneficiary forms (as in insurance policies and investment vehicles) can override THAT, but absent any of that (or gaps in the will) the status of "Married" will control. It could be a significant difference.
Another potential difference is in "next of kin" scenarios. I know that my stepson is in the Army, and the Army has strict guidelines as to who can be on base and who can "check him out" of his combat unit. So his live-in girlfriend cannot check him out, but she could if she was married to him. This can also rear it's ugly head in hospital/care situations.
It's getting rarer now, but some companies still (and this is a result of the high cost of healthcare, not some social protest or moral stance) will not allow "girlfriends" (or I should say "partners") on healthcare plans. They have to be a dependent or spouse.
There are some tax differences (especially at the State level) but that's kind of case-by-case.
Most of these are surmountable one way or the other. I got into a philosophical argument with someone once (and it was that, as I am NOT against gay marriage) that one of the arguments in favor of gay marriage was specious, because almost everything (except the healthcare thing and the Army thing) was possible to achieve without the actual concept of "legal marriage".
I will leave the "psychological" impact or the impact on children to others who are more familiar than I on those subjects.