our exec board:

President
VP Moral (philanthropy & stuff along those lines)
VP Social (new member trainer)
VP Mental (Academics & cultural events)
Recording Secretary
Corresponding Secretary
Treasurer
Panhellenic Delegate
Membership Chairman
Formal Recruitment Chairman
COB Chairman
Social Chairman
Risk Management Educator


Non-Exec Positions:

Public Relations Chairman
Transitions Officer (Senior Program)
Etiquitte Chairman
Philanthropy Chair
Interest Group Coordinator
Head of Angel Support Board
Arrow Correspondent
Historian

We also have interest groups which the "Captains" of are considered an important position. The IGs get stuff done for the exec members so the exec members aren't so bogged down.

My chapter had the following list of officers when I graduated (I presume it's still the same):

Elected Officers:
Eminent Archon (President)*
Eminent Deputy Archon (Vice President)
Eminent Treasurer (Treasurer)*
Eminent Recorder (Recording Secretary)
Pledge/Member Educator (New Member orientation)*
Brother at Large (Brotherhood/Morale)
Social Chairman
Scholarship Chairman
Eminent Chronicler (Historian)*
Eminent Chaplain
Eminent Herald (Ritual/Communications)
Eminent Warden (Sergeant at Arms)
Eminent Correspondent (Corresponding Secretary)
Recruitment Chairman
Fundraising Chairman
Philanthropy Chairman

Appointed Officers:
Risk Manager
Alumni Relations Chairman*
Assistant Pledge Educator(s)
Athletics Chairman
Greek Council Representative (and Alternate Rep)*
InterFraternity Council Representative (and Alternate Rep)*
Advertising Chairman
Song Chairman
Awards Chairman
Bylaws Committee Chairman*

*Note that those officers listed in bold are those minimally required by SAE's national laws. The first eight elected officers listed consituted my chapter's executive board. I had the opportunity to serve (officially or unofficially) in those positions listed with an '*'.

There were also the following boards/committees:

Judicial Board
Alumni Relations Committee
Bylaws Committee
Risk Management Committee
Scholarship Committee
Social Committee
Finance Committee
Auditing Committee
Ritual Committee

There are also opportunities to get involved in either or both of the InterFraternity and Greek Councils (depending on how the Greek system on any given campus is arranged).