Seam rippers

People who don't sew might not know of a handy little tool called a "seam ripper".  It's a small pointed blade that allows you to take out one stitch at a time without damaging the surrounding fabric.  These are cheap -- about $2 retail -- and if your seam ripper keeps you from ruining one article of clothing, it pays for itself.  (If you can recognize one by sight, you might even know to snag one for a quarter at a yard sale).

Here's a delicate sweater whose tag was too scratchy, with my little seam ripper getting ready for action.

I poke the tip of the blade through one of the stitches and then slide the seam ripper forward.  It cuts just the thread, not the surrounding fabric.

Here's a close-up of why this works.

With a seam ripper, you can remove scratchy tags, fix sewing mistakes, or even take off decorations that have stopped being decorative:  silly belt-loops, faded fabric flowers, buttons, etc.  Sometimes that's all you need to do to make a piece of clothing look good again.