A water-soluble or water-dispersible copolymer comprises copolymerized units a) of at least one ethylenically unsaturated monomer with a saccharide side group and b) of at least one hydrophilic ethylenically unsaturated monomer different from (meth)acrylamide, where the weight fraction of the ethylenically unsaturated monomers with a saccharide side group is 5 to 95% by weight. The copolymers exhibit high affinity to inorganic surfaces or hydrophilic fibers, such as cotton. They serve as soil release and/or graying-inhibiting polymers in textile detergents or minimize the risk of microbial colonization of materials coated therewith.