I have read that one should not have any material between one's tefillin shel yad and one's arm (e.g. bracelets, wristwatches). I always wear a wedding ring on the fourth finger of my left hand. I was taught to wrap the tefillin shel yad strap twice around my third (middle) finger, then once around my fourth (ring) finger. That means that the ring is between the strap and my finger. Is this permissible?
I was told that as you don't really have to wrap anything on your hand (it could hang loose from your mid-arm), it's not a problem. And I see plenty of good Jews who wear tefilin over their wedding bands.
Some even wear it over their wristwatches! I'd heard Rabbi Dovid Gottlieb (before he made aliyah from Baltimore) discuss this one, indicating there were multiple opinions on it.