When I first started traveling, I carried a Moleskine notebook in my pocket. I thought I was pretty hip, and it was really useful: you should always have a notebook and pen handy. But then I started to sweat, and the Moleskine wore out really quickly. The finishing blow was when I walked up Mount Fuji; never mind that the notebook was in a plastic bag, the rain turned it to pulp.
At the same time, I hadn't brought anything with me big enough to be used as a daily journal, and I was seeing so much that I regretted not writing about. Writing on the computer was far too impersonal, and, besides, by the time I could open up my laptop, the moment had often passed.
So, having learned my lesson, I bought a few Rite in the Rain waterproof paper notebooks, and I've never looked back. These things are absolutely incredible. I once tore out a page, wrote on it, and then ran it under the kitchen faucet for five minutes. The paper didn't get soggy, and the ink didn't run at all. My little green memo book is a permanent fixture in my back pocket, and hardly shows any wear after a year and a half.
I filled up my first all-weather travel journal in six months; it was the perfect size to pull out during while traveling by train or bus and do a little reflection.
The final ingredient is a pen that will work with waterproof paper. I carry the "bullet" style Fischer space pen, which is small enough that it fits in my wallet, yet as long as a normal pen when opened. All in all, carrying a waterproof memo book and bullet pen have saved me a lot of frustration on the road.
So, get out there and write! People will quickly get tired of looking at your pictures, but you can tell a good story over and over again.