Ostello Bello in Milan asks for your favorite song. You could follow this up by playing that song the next time they come into the common room. This could also work with favorite movies if you do regular movie nights, or favorite food if you want to organize a cook-up and want to make sure people will want to participate.
A lot of places throw in "How did you hear about us" to see which of their marketing efforts are paying off and which of the hostels in other cities are supporting them the most.
The most interesting question on my government-issued forms is "Purpose of you visit." They just want something general like business or tourism, but our guests tend to get creative. :D
You probably don't want your guests filling out forms for half an hour when they arrive, but if you just want to make it more interesting you could even throw in a photo hunt/spot the difference challenge like this one: