Part of my job is hardware support of PC's and Server equipment. It is a very good practice to ground yourself when working on equipment. For those that say you have never hurt your equipment before, you may be correct.. And you also may be wrong. Unfortunately, the damage can be done to chips without being noticeable for months... (Really, no kidding) Then all of a sudden the chip goes kaplooey. (Technical term that i may just copyright soon. :O)
Anyway, grounding is a good idea, but if you don't plug the PC into the wall socket you are not truly grounded at all and have wasted your time with the alligator clip... The ground must be plugged into a wall socket to work, so here is a trick I learned years ago. Take a standard three prong plug and remove both prongs from it with a pair of pliers.. Be sure to LEAVE the ground prong.. Now when you plug it in, only the ground is plugged in and your machine is fully grounded. Now take your gator clip and clip it to the frame of the machine. (Don't trust the floppy drive as you may not have a good connection to the frame... Also you don't know if the floppy is aluminum.. If it is you won't get any ground off it.)
