Which civilian airport has the most runways (current and planned)?
Chicago O'Hare International Airport (ORD) today has 8 runways, which is more than any other current airport has. In 2015 14L/32R was closed and 10R/28L was opened, and further runway changes are foreseen.


Beijing Daxing International Airport will be Bejing's third airport (planned to open in September 2019). According to Centreforaviation it will have 9 runways. One runway will be reserved for military use. The ninth runway is not visible on public maps and illustrations at this moment.


Denver International Airport (DEN) currently has 6, but the long term master plan foresees 10 runways in total by 2030, and 12 beyond 2030. See Jonathan Walters' answer for images. (Fun fact: there are a plenty of conspiracy theories about the shape and size of DEN)
Additional runways are not necessarily used to increase (commercial) traffic. Runways maybe reserved for different wind directions, to separate different type of planes (military, general aviation), or for noise abatement. This was already discussed better in the other question that you mention.



As an example for the noise abatement,  this picture (from LVNL) shows a snapshot of active runways at Amsterdam Airport Schiphol. There are 6 runways, of which usually only 2 or 3 are used. The most distant runway (here in green) is almost always in use, causing very long taxi times in favour of reducing the noise exposure of nearby residential areas.