Each subspecialty has a big meeting of their own or two or three. Then there are umbrella organizations.
The general ones I can think of that people go to:
ACS Clinical Congress (october) -- Huge meeting, has a lot of breadth, less depth, but generally a lot of fun
ACS spring meeting (March) -- less well attended, this year was held concurrently with SAGES and AHPBA
AAS (Association for Academic Surgery) (November)
www.aasurg.org -- this is a more junior society to SUS, but the level of research is actually pretty good. A good place to meet up and coming attendings
SUS (Society for University Surgeons) (Feb)
www.susweb.org --generally more senior surgeons in academia.
NOTE: AAS and SUS are trialing a joint meeting for 2006 in Feb.
www.academicsurgicalcongress.org
Specialty ones:
SSO (Society for Surgical Oncology) (Mar)
www.surgonc.org
SAGES (Society of American Gastrointestinal and Endoscopic Surgeons)
www.sages.org- (Mar): tends to focus on laparoscopy
ASCRS (American Society of Colon and Rectal Surgeons (May)
www.fascrs.org
AHPBA (American Hepato-Pancreato-Biliary Association) (Mar)
www.ahpba.org
AAES (American Association of Endocrine Surgeons) Apr or May
www.endocrinesurgery.org
SVS (Society for Vascular Surgery) (June)
www.vascularweb.org
there are also trauma, critical care, and thoracic and cardiac meetings. I'm getting bored with making this list, someone else is free to add to this.
Then there are tons of regional meetings: Central, Western, Pacific, Southern, Southeastern, Southwestern, etc. etc.