Spiral staircases may be an option for your residential applications where you can’t fit a conventional staircase. These are the rules from the 2006 International Residential Code.
Spiral staircases have to be at least 26″ wide with each tread being at least 7.5″ deep when you’re 12″ in from the narrow end. The treads have to have identical (uniform) dimensions and a rise of no more than 9.5″. You also have to provide a headroom of at least 6′-6″.
You can use spiral staircases in limited commercial applications where the space it serves is no more than 250 square feet and doesn’t serve more than 5 occupants. You can also use spiral staircases to access theater galleries, catwalks and gridirons. Beyond that spiral staircases are for residential use only.
The trick with spiral stairs is coming up with a combination of these dimensions that ends up facing the right direction at the top and bottom of the stair. Just because the rise and run work out doesn’t mean that the direction will work out. You can go as steep as 9 risers per turn but you’ll likely need to ease that to help you end up pointing the right direction. If you are creating a stair with more than 10 risers per turn you’ll need to start increasing the diameter of the stair where you’ll have the minimum tread depth.
Update: for the newer building codes, these are the code sections. R3126.96.36.199 in 2012 IRC and R3188.8.131.52 in 2009 IRC.