My wife and I are both very secular. We were together for about four years before we decided to get married and then another year before we actually did. There were basically two reasons why we did it.
1. There are obvious legal and financial incentives which lead to our decision to have a legal marriage. You can easily share property, finances, death benefits, etc. Being able to jointly own property without doing a ream of paperwork as well as be on each others insurance was quite useful. After a few years our finances were already very intertwined and both of us had supported the other through periods of unemployment. It had become impossible to separate our personal successes and so we decided to essentially merge our financial and legal entities. Some married couples keep separate bank accounts and maintain a lot of separation, but we did not.
Also, a pair of people is far more stable than an individual. As I mentioned we have supported each other through unemployment and I supported my wife when she became ill. From a purely economic and social standpoint our marriage is a way to hedge our risks. I support my wife when she struggles and I know that she will support me if any ill ever befalls me.
2. We wanted to proclaim and strengthen our bond through a marriage ceremony. This was the reason we decided to do a social marriage. We felt that there was value in clearly proclaiming our intent to live together indefinitely in front of our family and friends. The act of clearly stating something out loud to witnesses can have a powerful psychological effect and it forced us to confront any doubts we had and think into the future to decide whether the course we were on was really one we wanted to pursue. Basically, the marriage prevented us from simply coasting into the future and forced us to make a clear and conscious decision about what we were doing and then we reinforced it by announcing that decision publicly.
So there are real benefits to having a marriage which are entirely non-religious. I do sometimes wonder about the gender issues and what is biological vs. rational. We do not plan to ever have any children, so our marriage isn't to provide a stable environment for them.