Thats pretty much an old movie but I cant forget the dialogue! Talking about the trust, many a times you become an e-victim of cross site scripts, cookie thefts, and well online redirects from secure to non secure sites to steal the credentials - either by clicking upon a tinyurl or googl like service or by some other obvious reasons. So its important to keep yourself secure/safe; especially when travelling I find it important as well as hard to keep myself and my transactions, especially financial transactions, anonymous and secure.
"There's only two men I trust. One of them is me. The other's not you" - Nicolas Cage, Con Air
To avoid certain surprising, full of spined-shocks, situations you can use certain methods to keep yourself secure.
TrueCrypt is a free open-source disk encryption software for Windows 7/Vista/XP, Mac OS X, and Linux; you can use TrueCrypt, which actually creates a virtual encrypted disk(your choice of encryption) within a file and mounts it as a real disk, where you can keep the stuff that you want safe and out of reach.
The 'real' stuff can be whatever you do on a daily basis, for isntance shopping, etc. The encrypted hard drive is useful in case your computer gets compromised, especially when using free hotspots, for instance on some airport terminal waiting for the "connecting-flight" to tug you in.
While browsing for a similar ware I came across this nice look-n-feel website that was discussing Tor project, an anonymity network software that enables internet anonymity by thwarting network traffic analysis. Though you can download and start running the software, but this method is "not recommended", not atleast on the website.
You can use Tor for browsing purpose but still I'd avoid banking credentials as much as I can; and use an ATM or phone to do that. Some countries/companies have strict policies against Tor, for instance the middle eastern region, where right now, I am on a project for a small duration.
Better, if your work offers SSH or a VPN mechanism for accessing your company's email, that'd be the best way to do it. Mine does that.
Well... whereever you are travelling, a clean computer is always a good idea; there are certain countries that take a full copy of drives; and even have strict policies regarding encryption software, for instance in China. Better would be to bring a computer with an empty or no hard drive and a Ubuntu CD. You can use Ubuntu to tunnel your remote desktop to your home computer.
Also, you can use openVPN. That way you can run all your traffic over the secure path.
Or you may set up an SSH server at home; so that you can create a secure session when in remote parts of the world. Note that some countries do not allow SSH and probably will block secure ports, so its possible to go through a different well-known port, 80 for instance; if its not too much for you.
Above all its a good practice to revise your "critical" passwords frequently, specially before and after a travel.
Have a safe browsing!