Our son's bris was an important ritual to us particularly because my husband is not Jewish. Our wedding was performed in the Jewish tradition but a bris makes a stronger statement about a family's intentions. A bris is a serious event, performed under strict Jewish law. For us, it clarified our relatively new family's values about religion, to ourselves and to our extended family.
What I found particularly interesting is the timing of the bris. Having been in bed for eight days, I was coaxed into getting up and dressing up. Because I was still weak, it was the easiest party I ever hosted! Somehow, my family organized everything.
A close friend of mine, our lay rebbe, convinced me that as a feminist measure, I should include a baby naming ceremony too. We did that after the bris (and nursing), and it added a more informal, sweet touch to the day.