Interestingly, it isn't online services that have enabled this so much as a lifestyle choice. We value travel and figured it was cheaper to run our startup in most parts of the world than it was in our origin city.
We don't use a lot of online services for our business. Biggest one is Gmail, really, and hosting. Things we couldn't take with us.
I run a virtual machine on my laptop and under it I have a server that acts as our "intranet server" and so all of the collaboration tools, etc run there. I also start servers periodically while developing something that will eventually run in the cloud to test it out before running it online.
We're geared to be able to work full time without access to the internet. We're expecting to be in places where there is no internet. However, for the past 3 years that we've been traveling we've had pretty much full time internet access so far. When we're without internet we use an ad-hoc wifi network so we always have our "local network" with us.
Other than what fits in the backpacks we just have a couple boxes in storage. The most stressful experience has been going over all of our stuff and getting rid of it until we fit in the laptop. That took several months of work and because many of the possessions had a history it was not easy.
But now, we can go anywhere anytime we want, just about. It is very liberating!
Am willing to answer most questions....