I suppose the question would be OS specific, so I'll take the following scenarios:
Winodows (NTFS)
OSX (HFS)
Linux (ext2,ext3,ext4)
Each operating system has it's default filesystem it operates os (OSX, I beleive, only has the one choice available). I've noticed some utilities out there for OS's to read different file systems (which obvisouly is NOT apart of the kernel), which got me thinking: Are filesystem operations a function of a driver (ie, potentially modular), or is it truly apart of the kernel?