I would like to store data using google protocol buffers (another serialized format would work, too), and then have an UI to browse that data. Is there a C++ framework/API that
Wireshark has a protobuf plugin that lets you visualize the contents of protobuf messages. I'd also dig in to the DebugString() in google/protobuf/message.h or message_lite.h (I forget which off the top of my head) and see if you can easily dress that up for presentation to a user.
http://code.google.com/p/protobuf-wireshark/
I was working on such a solution last year using Qt. Unfortunately, the application is not yet complete, but I think I was at the point where one could more or less successfully visualize data from a generic protocol buffer stream. You can check out the code at
https://github.com/oneamtu/QProtoViewer
Again this is not a out-of-the-box solution, and you'll have to work to make it fit your own needs/project. I'd be more than happy to help if you choose to do so.