What is the best way to store still photos and video when travelling?

One way is to carry a high capacity portable media player, and transfer photos directly from the camera (via USB) as you travel. Toshiba's Gigabeat S30 allows you to do this, and supports most cameras. It's also available in a 60GB version.

You can also transfer pics from your camera to an iPod, though you'll need to pick up a camera connector for around $50 (see the Apple-made model here).

Otherwise, you could buy a device dedicated to photo storage. Sony makes a 40GB one, and Epson has two very pricey multimedia storage products.