Hydrogel compositions are provided (a) that have a continuous hydrophobic phase and a discontinuous hydrophilic phase, (b) that have a discontinuous hydrophilic phase and a continuous hydrophilic phase, or (c) that are entirely composed of a continuous hydrophilic phase. The hydrophobic phase, if present, is composed of a hydrophobic polymer, particularly a hydrophobic pressure-sensitive adhesive (PSA), a plasticizing elastomer, a tackifying resin, and an optional antioxidant. The discontinuous hydrophilic phase, if present, is composed of a crosslinked hydrophilic polymer, particularly a crosslinked cellulosic polymer such as crosslinked sodium carboxymethylcellulose. For those hydrogel compositions containing a continuous hydrophilic phase, the components of the phase include a cellulose ester composition or an acrylate polymer or copolymer, and a blend of a hydrophilic polymer and a complementary oligomer capable of hydrogen bonding thereto. Films prepared from hydrogel compositions containing or entirely composed of the aforementioned continuous hydrophilic phase can be made translucent, and may be prepared using either melt extrusion or solution casting. A preferred use of the hydrogel compositions is in wound dressings, although numerous other uses are possible as well.