Are the Nawaafil prayers to be prayed in two, three, or four Rak'ah

Imaam al-Shaafi'i and Maalik say that the optional prayer of the night and day are prayed in two Rak'ah. You say Salaam after every two Rak'ah. There evidence is the following hadith:

It was narrated from Ibn ‘Umar that the Messenger of Allah (sallallaahu alayhi wa sallam) said:

"The night prayer is (to be offered) two by two."

[Sunan Ibn Maajah Hadith No. 1380]

Abu Hanifah says that if you wish you can pray two Rak'ah, three Rak'ah, four Rak'ah, six Rak'ah, or eight Rak'ah without separating between them with a Salaam. His evidence is the Zaahir of the following (a)hadith:

Narrated Abu Salama bin `Abdur-Rahman:

That he asked `Aisha "How was the prayer of Allah's Messenger (sallallaahu alayhi wa sallam) in the month of Ramadan?" She replied, "He used not to pray more than eleven rak`at whether in Ramadan or in any other month. He used to offer four rak`at, let alone their beauty and length, and then four rak`at, let alone their beauty and length. Afterwards he would offer three rak`at. I said, 'O Allah's Messenger (sallallaahu alayhi wa sallam)! Do you go to bed before offering the witr prayer?' He said, 'My eyes sleep, but my heart does not sleep."'

[Sahih al-Bukhaari Hadith No. 3569]

The above mentioned tradition [this portion does not refer to the hadith above but to the hadith in Sunan Abi Dawud before this one] has also been narrated by Qatadah through a different chain of narrators. This version adds:

He used to pray eight rak'ahs during which he did not sit except in the eighth rak'ah. He would sit, make mention of Allah, supplicate Him and then utter the salutation so loudly that we could hear it. He would then pray two rak'ahs sitting after he had uttered the salutation. Then he would pray one rak'ah, and that made eleven rak'ahs, O my son. When the Messenger of Allah (sallallaahu alayhi wa sallam) grew old and became fleshy, he offered seven rak'ahs of witr, and then he would pray two rak'ahs sitting after he had uttered the salutation. The narrator narrated the tradition to the same effect till the end.

[Sunan Abi Dawud Hadith No. 1343]

Another group has said that the optional prayer of the night is to be done in two Rak'ah whereas the optional prayer of the day is done in four Rak'ah. 

Reference(s):

بداية المجتهد ونهاية المقتصد
Volume 1 Page 217