This is actually a very complicated issue. Let's try to frame the variables:
1. How many images do you expect to capture?
2. What format will you be shooting (RAW, RAW+JPEG, JPEG) and how big are the files on average?
3. Do you need or want to edit or preview on the trip?
4. How concerned are you about the possibility of losing some or all of the images?
5. Do you have a weight concern or restriction?
6. What is your budget?
The basic options are to:
1. Use multiple memory cards and download when you return
2. Use a storage
device to download images along the way
3. Use a laptop with or without an external drive
Multiple memory cards have some risk in case they get lost or stolen. Plus the cost of multiple memory cards may be prohibitive based on some of the variables above. Also, the hardest part for me, is that you really can't do much with the images until you return.
The external storage devices that don't require a computer are pricey IMHO! You might as well buy a laptop.
I purposely purchased a small (3.5 lb) full powered laptop for travel. It is not much bigger than the dimensions of two stacked iPads. I download my images every evening to both my laptop and an external drive. I keep the external drive in a different bag during transit too. I purchased a refurbed model and it cost less than many of the external storage devices! Obviously, unless space and/or weight is an issue, that is the best solution IMHO. This approach also allows you to do some image selection or processing if you have time on the plane or train.
Hope this helps!