What are the most widespread heresies that have spread throughout the Islamic world?

Innovations (bid‘ah) cannot be enumerated, especially in the domain of fatwas, as this requires an independent and extensive study. Allah Almighty says: (And verily, this is My Straight Path, so follow it, and follow not (other) paths, for they will separate you away from His Path. This He has ordained for you that you may become Al-Muttaqun (the pious)) [Al-An'am: 153]; the paths are not limited. In the hadith (definition) narrated by Ibn Mas'ud (may Allah be pleased with him), the Messenger of Allah (peace be upon him) drew a line and said: "This is the path of Allah," then he drew lines to its right and left and said: "These are paths, on each path there is a devil inviting to it," then he recited the verse.

The closest resource that would benefit the questioner in knowing a large number of innovations is the book "Mu'jam al-Bida'" by Sheikh Ra'ed Sabri Abu Al-Alfah.