Submission Opportunities: Play Submissions Helper is SIU Playwriting's favorite resource for submission opportunities.
Membership Opportunities: The Dramatists Guild is the closest thing playwrights have to a union.
Chicago Dramatists is Chicago's oldest new play development laboratory. If you're in the Chicago area you can join as a Network Playwright; if you're not in Chicago, you can join as a National Network Playwright. Membership includes many benefits, including a script critique program.
The Playwrights Center in Minneapolis also has a great set of resources, including another good source for submission opportunities and fellowships for playwrights.