Some method of keeping the camera dry is essential. The camera may be a disposable underwater cheapie, a regular camera with a waterproof container, a waterproof camera or a diving camera.
The waterproof container may be elaborate, or as simple as a double ziplock baggie.
Standard cameras make wonderful photographs, but not all kayaking pictures are worth keeping. Film development costs can be reduced to almost nothing with the use of digital cameras. With the digital camera, photos can be shared with friends across the internet, posted on homepages, or on KayakWiki. Paper copies of special photographs can be printed on a color printer or processed at a camera store, or even at a local shop's digital photo kiosk.
Waterproof cameras are typically rated to JIS7 (1m depth for 30 minutes), though there are a couple that are rated JIS8 (1.5m depth for 30 minutes). You may find others that can handle up to 5m depth for extended periods of time (suitable for snorkeling). Some waterproof containers for cameras have similar capabilities. Examples of such point-and-shoot cameras are (film) Pentax WR90 and WR105 and (digital) Pentax OPTIO WR33 and WR43. There are also other brands that are worth looking at. These kinds of cameras are perfect for sea and mild whitewater kayaking. They can take a dunk or roll and it is safe to rinse off saltwater by just holding it under a soft stream of fresh water.
Diving cameras and cases are designed for extended submersion to depths of 30m (100ft) or more. The architypical dive camera is the Nikonos - sadly, no longer made. Other brands are available at dive shops. Cases are made for a large number of cameras, both digital and film, and are relatively affordable. Canon, Olympus, Pentax, Sony and others make cases for their digital cameras that can handle 30m. Similar cases can be had for video cameras as well. These cases are often made of polycarbonate, a very tough plastic, and can handle rougher conditions and more violent submersions than a JIS7 rated camera.
If you are just looking for a tough and waterproof container to transport a camera, look at the better dry boxes.
If you want to enhance your ability to take pictures of water or of paddlers on water, consider a polarized filter for the camera.