I cut it in small triangular shapes and use it to mark the cutting slots on my June Tailor Shape Cut ruler. The triangle makes a little pointer so I don't get confused which slot to use. This also works on other rulers to help locate the line. I use it sticky side up (similar to suggested above) as a thread catcher. I just fold under the edges and stick it to the table rather than rolling into a ball. BTW - I use the wide tape for this. That's what I usually buy. It can be cut down to various widths as needed by sticking it on my mat (following lines to keep it straight) and using an old rotary cutter blade.
Lots of good suggestions here. BTW