What is the maximum distance between one's home and the mosque that necessitates performing the prescribed prayer in the mosque?

The correct view among scholars is that congregational prayer (salat al-jama'ah) is obligatory upon every sane, adult male, unless there is a valid excuse. Performing it in the mosque is a Sunnah (definition), not an obligation. He is required to answer the call for congregational prayer if he cannot perform it elsewhere. The mosque he is obliged to attend is the nearest one, such that he can catch the congregation after performing ablution and optional prayers at home, and walking at a moderate pace.