There are a number of options.
1. Buy a copy of Alcohol 110%. This is a program that lets you not only burn CD/DVDs, but make soft copies (an image file) of the cd/dvd that you can copy onto your hard drive. Then you use it on your notebook/laptop to mount the image and use it as you would if you had it in an actual drive. I like this option because, while it's a bit more involved, you can buy a LOT more hard drive space on a netbook for the money than you can in thumbdrives. The average netbook has between 250-500 GB of storage, and the mounted image will perform MUCH better than any thumbdrive.
2. Copying the DVDs to a thumb drive would take a separate thumb drive for each DVD. Otherwise you risk overwriting the menu structure and keeping things from working correctly.
3. There ARE small-profile external USB DVD drives out there.. Check Amazon, Frys, TigerDirect, and such to see what they have.
Other options depend on what device you want to carry. I just bought a Motorola XOOM tablet. Less bulky than a netbook, a bit more of a pain to type on, but for email, web browsing, and stuff you're likely to do on the road, it's very lightweight and easy to use gadget. It does not have an internal hard drive, but comes with a USB cable that allows you to connect an external hard drive. Alcohol isn't an option here, but there may be another similar option that I don't know about yet.
I have a 10" HP netbook that is twice the weight of the zoom, but has a huge hard drive and can contain any data I want to take on the road with me. Probably going to sell this once I have the XOOM set up.
Copying the DVDs to a thumb drive would take a separate thumb drive for each DVD. Otherwise you risk overwriting the menu structure and keeping things from working correctly.
Either a small portable hard drive or a thumb drive can be plugged into the either the XOOM or a netbook. You don't need to worry about how big a hard drive to buy; anything over 300 GB will probably store all the stuff you would want to take and all the videos/pictures you take along the way. With thumb drives, you have to be more concerned with space, as the tend to come in smaller sizes, and the 32GB and larger thumb drives start getting up there in cost with the portable hard drives with hundreds of GB of space. You can also buy HDs that are powered by the USB port, but your netbook may not provide enough power for it, so you'd still have to carry a power supply for it..
Confused? Welcome to my world..
