Before I begin remember Backup, ensuring you have a second copy of image incase the original is deleted, is different to Archiving, achieving dependable long term storage of an image.Buy more memory cards? Well they are getting almost as cheap as film, once you pay for its processing. For example a cheapest 4GB SD card I can find at the moment (in Australia) cost around $20. Many older camera can only take 1GB SD cards, which cost around $12. The table below will give you a rough guide to how many photos in jpeg format, fit on various card sizes given the camera's megapixel size.
Write CDs at the local photo booth. Most modern photo kiosks, especially in areas frequented by backpackers, offer a service to write a CD from files on your memory card. Often this is very cheap if you get a few photos printed. Rather than carry the CD around, why not post it to yourself (using a protective cardboard CD pouch).
Backpack drive, these are external disk drives, normally just temporarily connected to you computer(swapping between your home PC, laptop or notebook) via a USB connector. If you make sure this is relatively empty when you start you will have plenty of capacity for your trip.Today very large capacity 300 to 500GB are quiet affordable. It may be wise to invest a little more in a shock resistant model with its own travel case, as it will also be travelling with you.
USB Card Reader, even if you don't carry your own computer, having a suitable card reader will mean you could use the computers at a cyber cafe (but be warned not all of then will let you connect USB devices, sometimes they may charge you!) or those free library internet computers to transfer photos to your packback drive or even Skydrive.
A new type of Multi-media storage device for photographer is appearing, a kind of hybrid photo frame, card reader & backpack storage. At around $600 plus for 40GB at the moment, they are not cheap, eg. ten 4GB will SD cards be less than half the cost. Epsom seem to be leading this market in Australia.
Finally use Jpeg Format (rather than RAW) and consider shooting at a lower pixel size (if your camera allows this).