Yes. Linux uses the standard MS-DOS partitioning scheme, so it can share your disk with other operating systems.
Linux has loadable kernel modules for (presumably) all versions of Microsoft FAT and VFAT file systems, including Windows 2000 and WindowsMe. In a correctly configured system, they should load automatically when the partitions are mounted.
Note, however, that many other operating systems may not be exactly compatible. DOS's FDISK.EXE and FORMAT.EXE, for example, can overwrite data in a Linux partition, because they sometimes incorrectly use partition data from the partition's boot sector rather than the partition table.
In order to prevent programs from doing this, it is a good idea to zero out—under Linux—the start of a partition you created, before you use MS-DOS—or whatever—to format it. Type:
$ dd if=/dev/zero of=/dev/hdXY bs=512 count=1
where hdXY is the relevant partition; e.g., /dev/hda1 for the first partition of the first (IDE) disk.
Linux can read and write the files on your DOS and OS/2 FAT partitions and floppies using either the DOS file system type built into the kernel or mtools. There is kernel support for the VFAT file system used by Windows 9x and Windows NT.
There is reportedly a GPL'd OS/2 device driver that will read and write Linux ext2 partitions.
For information about FAT32 partition support, see http://bmrc.berkeley.edu/people/chaffee/fat32.html.
See, ("What Software does Linux Support?") for details and status of the emulators for DOS, MS Windows, and System V programs.
See also, "Can Linux access Amiga file systems? ", "Can Linux access Macintosh file systems? ", "Can Linux access BSD, SysV, etc., UFS? ", and "Can Linux access SMB file systems? "
There are said to be NTFS drivers under development, which should support compression as a standard feature.