I have MD 8.0 on a Laptop (Gateway solo) Does anybody know the best way to back up my files? I don't have a CD burner on it..or point me to any websites or howto doc.

You can always add a partition to your hard disk and backup your linux stuff to that partition. Of course, that isn't safe if your hd crashes.
Don't know how much stuff you want to backup, but linux does support zip drive backups. Zip drives are, of course, limited as to how much stuff they can hold. As far as I am able to find out, you cannot attach any USB external Hard Drive and expect it to work with linux. Chances are good that an ext HD attached to your serial port would work.

You could backup your hard drive to one of those backup services on the net. I have never tried this, so am not aware of how much it costs, how long it takes or anything else on the subject.

Another possibility is to network your laptop to a Desktop, if you have one, and to backup to tha HD on your desktop. There are several ways to do this. One way is to use software like laplink. Another is to network the two machines directly.

Probably none of this helps, but I thought I would give it a try.

Have a good day

What is the possibility of savin' certain files to a floppy and putting them on a desktop computer that has a burner?

You can save a limited amount of data to a floppy, that's true. But a floppy has only 1.44 MB of capacity, which doesn't go to far. But if you want to, this is a possibility, and then you can burn the data to a CDRW.
If you want to backup a little more data to disk, you could go out and buy a Zip drive. I think you can get one that holds about 250MB of data. Check out http://www.iomega.com