To find out what stairs you can currently challenge someone in, first go to the Main Stairs Page, then click on "Show your stairs only" link. The ones in BOLD are ones you can make a challenge in. .
Czuch Chuckers: I don't think there is a "list" anywhere, but if you know the person, you can go to their profile, click on the "Stairs" page.
In the "Step (your/max)" column, if it shows like "-/2", that means they are on retirement from that stair. If nothing shows up, it means they quit the stairs (but just finishing up their current games). For example, in my profile - I'm retired from a few stairs like the the swap 5-in-line stairs and such.