What are the risks of connecting an iPhone to an unsecured wireless network?
The iTunes Store uses HTTPS for most of it (if not all), at least that's how it was when I checked. 

Regarding your specific question, you have to consider the iPhone is another regular device, albeit full of limitations in the tweaking department, it still runs a OS X variant, with derived UNIX parts, etc. So for the sake of this question, let's say your iPhone is a computer running some form of Unix Operating System; with that in mind, all the security risks that affect a computer are valid. Should the iPhone (and iOS) have a remote vulnerability, you would be exposed, just like your Macbook or your Windows computer or even your Linux Box. 

Using 'open' Wi-Fi means anyone can log in and inspect the traffic. Anyone trying to do malicious stuff will be eavesdropping and listing for traffic in the network. 

If you send an email, it will likely be unencrypted and visible. If you use IM (MSN, Yahoo, iChat/AIM, Jabber, etc.) you are likely not encrypted either (nor using a secure channel by default). 

When using Safari, anything that doesn't go though some form of HTTPS is visible. Cookies and Data, with all the associated risks. 

So as you can see, and excluding particular OS vulnerabilities, we're very exposed when using open networks. Most people doesn't really care or know but the risks are there (and so are the malicious users) :)

Connecting through a VPN will help with your traffic, but I have never used a VPN on an iPhone and thus I don't know what the capabilities of that are.