Alternative to arrowroot
Corn starch (aka cornflour) will usually work and is more readily available, but it won't work well for acidic sauces, where you'll want to use tapioca starch.  (aka. cassava flour; if all you can find is tapioca in granule form, grind it up first).

For a more thorough list of starch based thickeners and their alternatives, see Cook's Thesaurus: Thickeners