For clothing, place the garment in the freezer for several hours and then peel off the bits. Cover it with a piece of wax paper then run a warm iron over top, the remainder should melt into this paper. You could also try pouring boiling vinegar over top to help it dissolve (This works even for gum that has been washed and dried in the laundry).
If you had the misfortune of finding it on your Carpet then use an ice pack to freeze it and pick out the brittle bits. You could also try covering the spot with a teaspoon of peanut butter. Allow it to sit for a minute or two, then lift up with a wet cloth. Clean the area with a wet, soapy cloth