I use Internet Cafes or some personal computer at the destination I'm travelling to. Computers have started to become a security issue when travelling internationally and I don't want the extra hassle. Internet access when travelling internationally is dependent on local access to WiFi or a hard wired connection anyway.
I have travelled with just a 500G external hard drive with reference documents, programs and storage space for photos, and that was a lot more compact than a full computer. About the size of an iPhone in fact and no batteries to charge. But for people that spend more time on their computer than their bike - that wouldn't work.