Even though you are connected to a free (and I take it "Open" WiFi), as long as you use your browser to connect to secure sites (the URL starts with an https://... and they have a little padlock on the bottom on the window), then everything that you send over the WiFi is encrypted and so is secure. You should avoid sending sensitive information in emails (in any circumstances) as they are not encrypted nor secure.
The main vulnerability is with spyware and viruses like keystroke loggers that look for your passwords or credit card details to send over the internet to their masters. A good virus protection and firewall package like ESET will prevent that, as long as you keep it up to date and let it complete it's regular scans.
Finally, Avoid paying bills using computers that you do not trust such as internet cafes as they could very well record your sessions. And remember, avoid clicking on this emails from people to look at their photos, visit a cool website etc. With that done, you should be fine, and much safer than paying a restaurant bill with your credit card!