I've heard of an interpretation that makes sense that I'll share here.
The key is verse 5....
I Corinthians 11:5 (ESV)
5but every wife who prays or prophesies with her head uncovered
dishonors her head--it is the same as if her head were shaven.
Let's define, "her head".
1 Corinthians 11:3 (ESV)
3But I want you to understand that the head of every man is Christ,
the head of a wife is her husband, and the head of Christ is God.
In Paul's day the cultural mores were such that if a woman were to attend public gatherings without a veil of sorts she would be regarded as an immodest woman. This would clearly dishonor her "head" or husband. So Paul admonished these women to wear their veils in addition to their long hair so that their husbands not be dishonored by them appearing immodest in public.
It could be argued that the "head covering" isn't required in our society but the principle of a woman being modest so as to not dishonor her husband publically is. The issue that comes into question is...how is modesty defined in one's cultural context? If living in an Eastern country where head coverings still apply, the principle would back up head coverings. If in a culture where head coverings do not apply, but perhaps a wedding band would, the principle would back up wearing a wedding band so as not to appear to be a loose woman and thereby dishonoring a woman's head or husband.
Just something I thought I'd include here.
For a while my wife wore something in her hair every time she was on the platform. It was something that we led our family into doing voluntarily. But as time passed I realized that the head covering wasn't so much the issue...the issue was deeper. Paul was calling women to honor their husbands through modest appearance in public.