It bothers me to do so. I associate the presence of something in my inbox with a feeling of pressure and obligation to respond to it. This applies to email and other similar services, not just Formspring.
I also find that it's much more difficult to respond to something if I don't do so immediately upon receiving it, because I go from having a natural reactive impulse to go with and build off of, to just having a bunch of analysis and thoughts about it in different directions, without the clear sense of direction that my immediate reaction provides.
I tend to only keep something in an inbox if I regard it as important and really intend to get back to it at some point in the near future. Otherwise, my general approach woud be to delete it, or store it away in a different folder, if that's an option, which it isn't with Formspring.
Oddly, despite all this, I do have a couple of questions besides this one sitting in my Formspring inbox. I found them interesting but didn't have an immediate answer, and I wasn't sure how much I'd be using Formspring going forward, because most of my online focus has switched to Facebook and Twitter, lately.
But your question did an excellent job of calling my attention back in a way that's giving me some new ideas about how to better integrate Formspring with the rest of my online activity, and I find these new ideas shiny and fun to play with at the moment. So thank you very much. :)