I think your question is really about the dangers of using public WIFI networks, especially to perform financial transactions. I started to write a really long reply explaining the dangers, and then I found This Article
which does a pretty good job of explaining the issues.
Most of the risks the article talks about occur in places with a lot of traffic, like airports and large coffee shops. When I am on the road, I use the campground WIFI or the coffee shop wifi if a) they require a password for me to log on to the network and b) I always use https
as the protocol. This ensures the information that is exchanged between you and the bank is encrypted. Most browsers will show a locked padlock icon when you are using https.
Some banks are now implementing two factor authentication. After you enter your user id and password, they will send a text message to your cell phone with a several digit number. Then you have to enter that number on your computer before you can view your accounts. It is less convenient, but more secure since whoever is accessing the account has to have your cell phone as well the other information.
Not related to computer security, but one precaution my wife I have taken is to establish a second checking account that is used only when we are traveling. This checking account is not linked to our savings account or our credit card, and has its own debit/cash card. We keep a relatively small amount of money in this "travel checking account" so that if the cash card is somehow compromised (e.g. by using a bogus ATM), the thieves would not have access to all our money at the bank.
Hope this helps.