Q: Is there a way to password protect only certain iPhone apps?

You mean something like web watcher or net nanny?  Most websites don't consider basic information to need protecting so they don't require a password for the home page.  But many require a password for more involved interaction like subscriptions or purchases.  Maybe I should ask who you are concerned might gain access to an important non protected website and what information you are concerned about.  Also, Safari and other web browsers memorize passwords for websites to make your life easier and it these are in place, you at one time gave the browser permission to remember the password on a device.  But Safari shares this information across platforms.  Do you need help getting Safari to prompt for a password again for some sites?  What are some example sites?

Bill Pride wrote:

 

I have have a password to unlock my iPhone, of course.  And if an app opens a website that requires a password, I enter it after the app brings up the websitet  But some websites don't require a password to get in.  Can I add a password layer to the app itself the blocks it from reaching the website unless a password is entered?

Unless the website or app itself - like an email or bank site asks for a password - the short answer is No - there is no intrinsic ability of the iPhone features that lets one do what you are looking for

Use Guided Access with iPhone, iPad, and iPod touch - Apple Support

Bill Pride wrote:

 

I suggest it would be a product enhancement that will come eventually, if Apple hasn't included it yet.

Apple doesn't read here for suggestions but they do have a feedback site:

http://www.apple.com/feedback