Use the DOS file system, type, for example:
$ mkdir /dos
$ mount -t msdos -o conv=text,umask=022,uid=100,gid=100 /dev/hda3 /dos
If it's a floppy, don't forget to umount it before ejecting it!
You can use the conv=text/binary/auto, umask=nnn, uid=nnn, and gid=nnn options to control the automatic line-ending conversion, permissions and ownerships of the files in the DOS file system as they appear under Linux. If you mount your DOS file system by putting it in your /etc/fstab, you can record the options (comma-separated) there, instead of defaults.
Alternatively, you can use mtools, available in both binary and source form on the FTP sites. ("Where Are the Linux FTP Archives?")
A kernel patch (known as the fd-patches) is available which allows floppies with nonstandard numbers of tracks and/or sectors to be used; this patch is included in the 1.1 alpha testing kernel series.