I am the new president this year (after 2 years as Hospitality chair) and our past president is a voting member of the executive board. I wouldn't have it any other way because I value his insight. I'm currently trying to talk him into being a chair of another committee.
I am the past VP and Pres at our school, I now serve as the secretary and the President appointed me Volunteer cooridanator. There is no correlation to this, no one else wanted to do and I was nominated by the committee.
Ours serves as a non-voting member of the Board and chairs the Nominating committee (per bylaws).
As past prez, he/she is available to provide expertise and continuity, but has no specific day to day responsibilities (besides nominations).
But many people on our Board do double duty, so a past prez may sign up to be a committee chair. In that case, he/she would have a vote for THAT position.