Forget that we're talking about wifi, and instead pretend you're giving your personal information (cards, fingerprints, whatever) to an intermediary who will go to your bank and pay in or withdraw money for you. Let's say you'll give them your money, and it will be in a sealed envelope. Would you choose as this intermediary (1) someone you know and trust; or (2) someone you've never met and know nothing about and who will be your courier for free. Clearly you would use someone you trust, in the same way and for the same reasons that you should use network connections you trust. Indeed, piggybacking on unsecured wifi is arguably even worse than (2) as what you're really doing is forcing this unknown person to handle your private information whether they like it or not. You haven't even asked first! As for the money in a sealed envelope, whenever you use the internet you're transmitting data. Some of it is more sensitive than the rest. All of it is transported in packets. Subject to certain caveats, these can be opened and read by anyone with access to them. This includes anyone who controls a wifi network that you use (or a third party who has compromised a network that was insecure).
Read something like this for a guide as to how you can mitigate risks.
Assuming you don't use a Microsoft web browser,
the EFF's HTTPS Everywhere extension is a really helpful starting point in mitigating some of the most obvious dangers, too.
The best advice of all, though, is that you shouldn't use unsecure wifi, for exactly the reasons that you wouldn't give control of your money to that stranger.