A re post from another place:
Rom walton says Boinc needs the following:
BOINC Manager needs to be able to open outbound connections to either 1043 or 31416.
BOINC Screensaver needs to be able to open outbound connections to either 1043 or 31416.
BOINC needs to open an inbound connection to either 1043 or 31416, and an outbound connection to port 80 for downloads and uploads of workunits, results, and science packages.
edit 17/12/05: BOINC may also need port 43. CPDN Trickle's may ned https on port 443.
K.