What roles are women allowed to play in LDS Sunday services? On a Sunday when a Latter-day Saints congregation meets, what roles are women allowed or not allowed to play in the service?
Well, so the big hidden question here is "what comprises an LDS sunday service?".  A related question covers some of this, so I'll just summarize.  In your average "Sacrament meeting", you'll typically have:


1 who presides at the meeting
1 who conducts the meeting (may be the same as the one presiding)
1 who leads the music
1 who plays the piano/organ
2+ who bless the Sacrament (Eucharist)
several who pass the Sacrament to the congregation
2 who say the opening and closing prayers
several who give short talks or sermons


Of these, the only thing women may not do is preside at the meeting, bless the Sacrament, or pass the Sacrament.  Those are duties of people who hold the Priesthood, and only men hold the Priesthood.

It would be very unusual to see a woman conduct the meeting, since that is usually done by the presiding person or one of his counselors.  However, there are some meetings of the Church where women conduct the meetings (for example, the General Relief Society Meeting).  There are also meetings where women preside (again, most meetings of the Relief Society), but that does not happen in a Sacrament meeting.