One big advantage of a poster session is that it means that people who don't give talks can still present their work to a wide audience, and it also gives them a feeling of participation in the conference; they are no longer just passively watching the talks, they are active in the mathematical activity of the conference. In short, it made me feel worthwhile and that I had done something useful there, rather than just hanging out in Burlington, VT.
(I also got to meet former YMN editor Emil Volchek there, but this is not guaranteed to happen at conferences with poster sessions).
From discussions with friends in other scientific disciplines, it seems that at their conferences poster sessions are commonplace, whereas in mathematics they are comparatively rare (the Joint Meetings in Phoenix, AZ in 2004 had them, but I can't think of any other math conferences that have them). Does anyone know why mathematics doesn't have poster sessions?
Chawne came up with some really useful comments on posters in mathematics.
One problem is that some people feel that they have to put their entire paper into the poster. This leads to a rectangular block of pages full of 8-point text, which is clearly not visually attractive.
To help you poster avoid these pitfalls, here are some links which may help people produce a better poster.
Chawne also pointed out that there were lots of poster sessions at the Joint Meetings in Phoenix in 2004; the YMN session, the AWM session (for postdocs and graduate students), an NSF session spotlighting the efforts of the undergraduate division of DMS (where PIs presented posters on their NSF-supported projects like REUs and curriculum reform) and an MAA poster session for undergraduates.
The SIAM July 2004 meeting also has a poster and symposium session.
So there are poster sessions out there.