WiFi (wireless internet) can be dangerous, but so long as your doing your banking with a reputable bank, and they use an SSL Page that’s secured (you’ll see a little lock icon in the bottom right of your browser if the webpage is secured, it’s completely safe as it’s encrypted. The stuff that is not encrypted can however be seen by anyone in the area. One area of trouble are email passwords. Most email passwords are sent in the clear.
A solution to this is using a program such as AI Roboform, in which you enter your login and password, and Roboform stores the information in an encrypted file, which it auto-fill the information from that point once you enter a master password.