Open cell mats, or self inflating mattresses as they are also known, have quickly become the most common thing to sleep on when camping. They are much more robust than traditional pvc airbeds and take up a lot less room in your tent.
When unrolled and the valve opened, self inflate mats suck air in as the foam cells expand. Thus they pretty much inflate themselves. You can also top up additional air with your mouth. They come in a variety of thicknesses from 2.5cm to 10cm. You can also purchase lightweight models for walking and trekking right up to deluxe double size models with built in pillows.