Yes, if enabled in the Control Panel there are 5 custom input areas for data retention (CP -> Users -> Registration -> Registration Screen Tab -> "Custom Fields" section).
Here we use them just for requesting your forum URL, but at my gardening forum I use them for asking about my users hardiness zones, gardens, gender, real name, plants, etc. I modified my input page (being the edit profile page) to allow a textarea for these fields (through code modification, which aren't supported from the vendor). One could also add additional fields if they were comfortable with editing code and the backend database (but again these changes are not supported by the vendor).
