You don't need webbed fingers to swim but it'll definitely help you swim faster. The Speedo Aquafit Swim Training Gloves ($22) gives you webbed fingers for better propulsion through the water. It also gives your upper body a great workout. Keep it up and soon enough you'll look like a swimmer. You may want to go slow if it's your first time using webbed gloves because it's going to put a lot of strain on your muscles. When you're a little bit better conditioned, go all out.
See video below for an alternative to the Aqua Fit.