What functionality is only available when syncing to Windows or OS X? I'm considering buying an android phone (probably a Galaxy S variant).  But I only run Linux (Gentoo if it matters).  So, I'm curious what features work with Linux, and whether there are any features that I'll miss out on by not syncing my phone to a Windows or OS X PC.

(I'm being optimistic in the title and assuming that most things will Just Work -- please correct me if I'm wrong.)
As Trampster said, currently Samsung are only pushing firmware updates through their Windows-only Kies software. Many manufacturers push out the updates wirelessly "OTA" (over-the-air) straight to the phone, so never go near a PC, and some provide a file that you download onto the phone's SD card and then boot the phone into a special update mode, none of these have any desktop OS requirements.

Other than that most of Android is designed to sync with "the cloud" so Mail, Calendar, Contacts, etc all sync with GMail, social networking sites, and some 3rd party mail/calendar/contacts providers straight from the phone to the server.

Music, pictures, videos etc live on the micro-SD card in your phone which can be mounted as a drive on any OS that can normally mount USB drives. See this SuperUser question about mounting a Galaxy S on Ubuntu where it turned out to be much easier than the questioner thought What is the mount point Samsung Galaxy S for Ubuntu Desktop?

Apps either save their data to the SD card, sync to a server on the web, or (in very rare cases, but I do have one app that does this) sync via WiFi to a PC on the local LAN.

So, in general Android phones really don't care what your desktop OS is, as you'll rarely need to do anything other than connect it as a USB drive.