One solution is to buy a waterproof case for your camera. Specially-made rigid waterproof cases are available for many popular compact cameras, and even for some super-zoom models. These are usually available from the camera manufacturer, although there are some third-party companies that make them too. These cases are totally waterproof, and many are rated for use underwater at depths as great as 40 metres. They offer a high degree of protection, but at around Â£100-Â£140 they are quite expensive and are a bit of an overkill for a mere rain shower.
For digital SLR users one option is the AquaTech range of weatherproof camera covers, used by many professional sports and wildlife photographers. They are made from the same type of breathable waterproof fabric as your anorak (yes, we know you have one), with zipper and velcro closures and a waterproof seal around the lens barrel to ensure your camera stays snug and dry even in heavy rain. They aren't cheap, costing Â£60 for the basic model and Â£160 for one to fit a long telephoto lens, but they are very effective.
Another type of waterproof case more suitable for owners of compact or super-zoom cameras is the Aquapac. Made by a British company, Aquapac cases are available for a wide range of electronic equipment, from GPS units and walkie-talkies to mobile phones and of course digital cameras. They are made from a durable, flexible plastic with a patented waterproof clip closure, and provide protection against rain, spray, sand, dust and even immersion in water. They can also provide buoyancy if you happen to drop your camera in the water, which makes them popular with surfers, yachtsmen and others who muck about in the sea. Due to the effects of water pressure Aquapac cases aren't really suitable for for use at depths greater than a metre or so, but they are a lot cheaper than dive-rated underwater cases. Aquapac cases for small compact camera cases start at Â£20, and even SLR-sized cases are only Â£80.
There are other even cheaper solutions. Simply popping your camera into a see-through zip-lock plastic bag will protect it from the rain while allowing you to operate the controls and take pictures, although of course shooting through a sheet of polythene is going to have a negative effect on your picture quality. Pull the plastic taut over the lens before shooting to minimise the distortion and internal reflection, especially if you use the flash.