There are more independent beliefs than just the Sunni and Shia, here are
some more:Wahhabi- Salafi/Wahhabi: Their beliefs are based on the Quran, hadith and sunnah (for the most part accepted by Sunni), fiqh etc. and the opinions of the knowledgeable scholars of the traditions of the companions of the prophet passed down generations.
International community of Submitters - Their beliefs are based on the Quran alone, and understand God to be the teacher of the Quran and that the messenger of the covenant has been chosen by God and sent already to unify all Monotheists.
Ahmadiyya - Their beliefs are based on the Quran, hadith and sunnah etc. and the opinions of the awaited one (Hadhrat Mirza Ghulam Ahmad) and their leading scholars.
Sufi - Their beliefs are based on the Quran, hadith and sunnah (Sunni/Shia) etc. and the opinions of the teachers of the traditions passed down generations.
- Ismaili - Their beliefs are based on the Quran, hadith and sunnah (for the most part accepted by Shia) etc. and the opinions of their chosen Imam from the prophet Muhammad's progeny and their Ismaili scholars.
Dawoodi Bohra - Their beliefs are based on the Quran, hadith and sunnah (for the most part accepted by Shia) etc. and the opinions of their chosen Imam from the prophet Muhammad's progeny and their Dawoodi Bohra scholars.
Links and descriptions provided by Shareef Islam