I had exactly the same problem with my thumbdrive. It seems that the manufacturer formatted the drive without a partition table. To mount the drive, you could use this command..

su
mkdir /mnt/thumbdrive
mount -t vfat /dev/sda /mnt/thumbdrive
You can now work with the drive..
umount /mnt/thumbdrive (for when you're finished)

However a better solution would be to add a partition table to your thumbdrive, and reformat in fat32. Do note that this means the drive will NOT work in win9x anymore, and you will lose all data on the drive, for some reason win9x becomes confused if there's a partition table on a thumbdrive. Win2k and XP I have tested, and they work fine.
To repartition and format the drive do exactly this from Knoppix console (you will only have to do this once)

su (become root so you have permission)
fdisk /dev/sda (open the partitioning tool to work with your thumbdrive)
At the fdisk prompt you will see some errors, fdisk is trying to interpret the non-existant partition table.
Type 'o' to create a new partition table.
Then type 'n' to create a new partition, make it number 1, and leave the defaults as they are for the size (to use the whole disk)
Type 'w' to write the table and quit fdisk
Now we need to format the drive...
mkfs.vfat /dev/sda1 should do the trick...

Now you can use the icon on your desktop for sda1, the other icons won't go away until you restart.

Note that you only have to do this once, and from now on your thumbdrive will appear on the desktop whenever you boot. You should always unmount it before you remove it.

Hope that all helps somebody (I had to figure it myself =P)
Enjoy!