NCAA Division I athletic conference (
Division I-A for
football).
The Big East was originally formed in 1980 as a made-for-TV basketball (plus non-revenue sports) conference consisting of teams from major media markets. Football was not included; the few schools in the BE that had football teams fielded their teams as independents. However, as bowl games locked in alliances with conferences that kept independent teams (except Notre Dame) from ever getting a bowl bid, the conference added football to satisfy the growing contingent of football-playing schools. However, it kept certain schools added for football purposes only out for other sports and allowed others to keep certain sports of theirs out of the conference.
The legacy of this is a conference with varying degrees of membership. As of 2002, one school played football only; several didn't have Division I-A football teams (or teams at all, in some cases); one kept its national powerhouse baseball team out; one kept its historic independent status in football even as its program slides down the tubes, etc. (Some sports offered by member universities are not offered by the BE, but that's fairly common across all conferences.)
The instability of the above arrangement should be pretty obvious, and it was all blown apart in the summer of 2003 when the Atlantic Coast Conference came calling. University of Miami had flirted with the ACC for several years, while Virginia Tech had hoped against hope for an ACC slot since that conference was founded. In late May, the ACC voted to begin expansion discussions with Miami, Syracuse and Boston College; the remaining five football-playing members of the BE sued, and several ACC players got cold feet as VT started working every political angle it could find to get an invite. In the end, Miami and Virginia Tech were formally invited in late June, to begin play in fall 2004; in October, the ACC finally decided on Boston College as its 12th, to begin play in fall 2005. The Big East then turned around and raided Conference USA, adding multiple teams from that league in hopes of maintaining its basketball reputation and Bowl Championship Series slot in football.
This remaining conference's fault line is perhaps even more pronounced; note that all the non-football schools are private and Catholic-affiliated, and of the all-sports schools, all but Syracuse are public (and Syracuse is a secular institution). I wouldn't place any bets on the continued stability of the post-2005 conference.